Seja f a função definida por f ( x ) = 2 + s e n ( 2 x ) f\left(x\right)=2+sen\left(2x\right) f ( x ) = 2 + s e n ( 2 x ) . Considera as seguintes afirmações: I. lim ⁡ x → + ∞ f ( x ) = + ∞ \lim_{x\rightarrow+\infty}f\left(x\right)=+\infty x → + ∞ lim f ( x ) = + ∞ II. lim ⁡ x → 0 f ( x ) − 2 3 x = 2 3 \lim_{x\rightarrow0}\ \frac{f\left(x\right)-2}{3x}=\frac{2}{3} x → 0 lim 3 x f ( x ) − 2 = 3 2 Selecciona a opção correta

Apenas a afirmação II, é verdadeira.

Apenas a afirmação I. é verdadeira.

As duas afirmações são falsas.

As duas afirmações são verdadeiras.

Seja a a a um número real tal que lim ⁡ x → π 4 s e n ( π 4 − x ) 2 x − π 2 = a \lim_{x\rightarrow\ \frac{\pi}{4}}\ \frac{sen\left(\frac{\pi}{4}-x\right)}{2x-\frac{\pi}{2}}=a x → 4 π lim 2 x − 2 π s e n ( 4 π − x ) = a . Seleciona a resposta correta.

a = − 1 2 a=-\frac{1}{2} a = − 2 1

Seja a a um número real tal que lim ⁡ x → 0 s e n ( 1 3 x ) x = a \lim_{x\rightarrow0}\ \frac{sen\ \left(\frac{1}{3}x\right)}{x}=a x → 0 lim x s e n ( 3 1 x ) = a . Seleciona a resposta correta

a = − 1 3 a=-\frac{1}{3} a = − 3 1

Qual é o valor de lim ⁡ x → 0 7 s e n x cos ⁡ x 2 x \lim_{x\rightarrow0}\ \frac{7\ sen\ x\ \cos\ x}{2x} x → 0 lim 2 x 7 s e n x cos x ?

− 7 2 x -\frac{7}{2}x − 2 7 x

Qual é o valor de lim ⁡ x → π 4 cos ⁡ ( 2 x ) s e n x − cos ⁡ x \lim_{x\rightarrow\ \frac{\pi}{4}}\ \frac{\cos\left(2x\right)}{senx-\cos x} x → 4 π lim s e n x − cos x cos ( 2 x ) ?

− 2 -\sqrt{2} − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Qual é o valor de lim ⁡ x → π 2 s e n x cos ⁡ ( 1 2 x ) \lim_{x\rightarrow\ \frac{\pi}{2}}\ \frac{sen\ x}{\cos\ \left(\frac{1}{2}x\right)} x → 2 π lim cos ( 2 1 x ) s e n x ?

2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

1 2 2 \frac{1}{2}\sqrt{2} 2 1 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 2 2\sqrt{2} 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 3 2\sqrt{3} 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

3 3 3\sqrt{3} 3 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Considera a função f f f definida por ramos Seleciona a resposta correta.

lim ⁡ x → 0 f ( x ) = 2 \lim_{x\rightarrow0}\ f\left(x\right)=2 x → 0 lim f ( x ) = 2

lim ⁡ x → 0 f ( x ) = 1 \lim_{x\rightarrow0}\ f\left(x\right)=1 x → 0 lim f ( x ) = 1

lim ⁡ x → 0 f ( x ) = 1 2 \lim_{x\rightarrow0}f\left(x\right)=\frac{1}{2} x → 0 lim f ( x ) = 2 1

Não existe lim ⁡ x → 0 f ( x ) \lim_{x\rightarrow0}f\left(x\right) x → 0 lim f ( x )

Qual é o valor de lim ⁡ x → π 4 cos ⁡ ( 2 x ) cos ⁡ x − s e n x \lim_{x\rightarrow\ \frac{\pi}{4}}\ \frac{\cos\left(2x\right)}{\cos x-sen\ x} x → 4 π lim cos x − s e n x cos ( 2 x ) ?

2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 2 -\sqrt{2} − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 2 \frac{\sqrt{2}}{2} 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 1 2 -\frac{1}{\sqrt{2}} − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1

Limites Trigonometria

Authored by Maria João Lagarto

Mathematics

12th Grade

Used 5+ times

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FILL IN THE BLANKS QUESTION

3 mins • 1 pt

Determina $\lim_{x\rightarrow0}\ \frac{sen\left(3x\right)}{x}$

(a)

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Qual é o valor de $\lim_{x\rightarrow0}\ \frac{5senx}{3x}$ ?

$\frac{3}{5}$

$\frac{1}{3}$

$1$

$\frac{5}{3}$

$0$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Qual é o valor de $\lim_{x\rightarrow0}\ \frac{x}{sen\left(5x\right)}$ ?

$5$

$\frac{1}{5}$

$1$

$0$

FILL IN THE BLANKS QUESTION

3 mins • 1 pt

Determina $\lim_{x\rightarrow\pi}\ \frac{sen\left(x-\pi\right)}{x-\pi}$

(a)

FILL IN THE BLANKS QUESTION

3 mins • 1 pt

Determina $\lim_{x\rightarrow0}\ \frac{tgx}{x}$

(a)

FILL IN THE BLANKS QUESTION

3 mins • 1 pt

Determina $\lim_{x\rightarrow\pi}\ \frac{senx}{x}$

(a)

FILL IN THE BLANKS QUESTION

3 mins • 1 pt

Determina $\lim_{x\rightarrow0}\ \frac{sen\left(3x\right)}{x}$

(a)

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Determina $\lim_{x\rightarrow0}\ \frac{sen\left(2x\right)}{-5x}$

$\frac{2}{5}$

$-\frac{1}{5}$

$-\frac{5}{2}$

$-\frac{2}{5}$

FILL IN THE BLANKS QUESTION

3 mins • 1 pt

Determina $\lim_{x\rightarrow0}\ \frac{4x}{senx}$

(a)

10.

FILL IN THE BLANKS QUESTION

3 mins • 1 pt

Determina $\lim_{x\rightarrow0}\ \frac{6x+senx}{x}$

(a)

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Limites Trigonometria

Determina lim⁡x→0 sen(3x)x\lim_{x\rightarrow0}\ \frac{sen\left(3x\right)}{x}x→0lim​ xsen(3x)​ (a)

Qual é o valor de lim⁡x→0 5senx3x\lim_{x\rightarrow0}\ \frac{5senx}{3x}x→0lim​ 3x5senx​ ?

Qual é o valor de lim⁡x→0 xsen(5x)\lim_{x\rightarrow0}\ \frac{x}{sen\left(5x\right)}x→0lim​ sen(5x)x​ ?

Determina lim⁡x→π sen(x−π)x−π\lim_{x\rightarrow\pi}\ \frac{sen\left(x-\pi\right)}{x-\pi}x→πlim​ x−πsen(x−π)​ (a)

Determina lim⁡x→0 tgxx\lim_{x\rightarrow0}\ \frac{tgx}{x}x→0lim​ xtgx​ (a)

Determina lim⁡x→π senxx\lim_{x\rightarrow\pi}\ \frac{senx}{x}x→πlim​ xsenx​ (a)

Determina lim⁡x→0 sen(3x)x\lim_{x\rightarrow0}\ \frac{sen\left(3x\right)}{x}x→0lim​ xsen(3x)​ (a)

Determina lim⁡x→0 sen(2x)−5x\lim_{x\rightarrow0}\ \frac{sen\left(2x\right)}{-5x}x→0lim​ −5xsen(2x)​

Determina lim⁡x→0 4xsenx\lim_{x\rightarrow0}\ \frac{4x}{senx}x→0lim​ senx4x​ (a)

Determina lim⁡x→0 6x+senxx\lim_{x\rightarrow0}\ \frac{6x+senx}{x}x→0lim​ x6x+senx​ (a)

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Determina $\lim_{x\rightarrow0}\ \frac{sen\left(3x\right)}{x}$

(a)

Qual é o valor de $\lim_{x\rightarrow0}\ \frac{5senx}{3x}$ ?

Qual é o valor de $\lim_{x\rightarrow0}\ \frac{x}{sen\left(5x\right)}$ ?

Determina $\lim_{x\rightarrow\pi}\ \frac{sen\left(x-\pi\right)}{x-\pi}$

(a)

Determina $\lim_{x\rightarrow0}\ \frac{tgx}{x}$

(a)

Determina $\lim_{x\rightarrow\pi}\ \frac{senx}{x}$

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Determina $\lim_{x\rightarrow0}\ \frac{6x+senx}{x}$

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