Evaluate lim ⁡ x → 0 x + 2 − 2 x \lim_{x\to0}\frac{\sqrt{x+2}-\sqrt{2}}{x} x → 0 lim x x + 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 <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 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

1 2 8 \frac{1}{2\sqrt{8}} 2 8 <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

Evaluate lim ⁡ x → π 4 tan ⁡ x − 1 sin ⁡ x − cos ⁡ x \lim_{x\to\frac{\pi}{4}}\frac{\tan x\ -\ 1}{\sin x\ -\ \cos x} x → 4 π lim sin x − cos x tan x − 1

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">

3 2 \frac{\sqrt{3}}{2} 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">

Evaluate lim ⁡ x → π 2 tan ⁡ x − cot ⁡ x sec ⁡ x \lim_{x\rightarrow\frac{\pi}{2}}\frac{\tan x-\cot x}{\sec x} x → 2 π lim sec x tan x − cot 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">

Evaluating Limits

Authored by Ryan Tamburrino

Mathematics

11th - 12th Grade

CCSS covered

Used 28+ times

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20 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate $\lim_{x\to5}1$ .

$0$

$1$

$5$

DNE

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate $\lim_{x\to1}5e^2-10\pi$ .

$5e^2-10\pi$

$-5$

$0$

DNE

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate $\lim_{x\to4}4x-1$ .

DNE

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate $\lim_{x\rightarrow0}\ \left(3x-2\right)^4$ .

$0$

$16$

$-16$

DNE

Tags

CCSS.HSA.APR.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evalulate $\lim_{x\to7}\frac{3x}{\sqrt{x+2}}$ .

$\frac{21}{9}$

$7$

$0$

DNE

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate $\lim_{x\to0}\frac{\sqrt{x+2}-\sqrt{2}}{x}$ .

$0$

$\frac{1}{2\sqrt{8}}$

$\frac{1}{2\sqrt{2}}$

DNE

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate $\lim_{x\to0}\frac{\sqrt{x^2}}{x}$ .

$0$

$\infty$

$-\infty$

DNE

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate $\lim_{x\to0}\frac{\sin^2x}{3x}$ .

$\frac{1}{3}$

$1$

$0$

DNE

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate $\lim_{x\to0}\frac{\sec x}{x\csc x}$ .

$0$

$1$

$2$

DNE

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.4

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate $\lim_{x\to0}\frac{3\left(1-\cos^2x\right)}{x\sin x}$ .

$0$

$3$

$\infty$

DNE

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSF.TF.A.2

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Evaluating Limits

Evaluate lim⁡x→51\lim_{x\to5}1x→5lim​1 .

Evaluate lim⁡x→15e2−10π\lim_{x\to1}5e^2-10\pix→1lim​5e2−10π .

Evaluate lim⁡x→44x−1\lim_{x\to4}4x-1x→4lim​4x−1 .

Evaluate lim⁡x→0 (3x−2)4\lim_{x\rightarrow0}\ \left(3x-2\right)^4x→0lim​ (3x−2)4 .

Evalulate lim⁡x→73xx+2\lim_{x\to7}\frac{3x}{\sqrt{x+2}}x→7lim​x+2​3x​ .

Evaluate lim⁡x→0x+2−2x\lim_{x\to0}\frac{\sqrt{x+2}-\sqrt{2}}{x}x→0lim​xx+2​−2​​ .

Evaluate lim⁡x→0x2x\lim_{x\to0}\frac{\sqrt{x^2}}{x}x→0lim​xx2​​ .

Evaluate lim⁡x→0sin⁡2x3x\lim_{x\to0}\frac{\sin^2x}{3x}x→0lim​3xsin2x​ .

Evaluate lim⁡x→0sec⁡xxcsc⁡x\lim_{x\to0}\frac{\sec x}{x\csc x}x→0lim​xcscxsecx​ .

Evaluate lim⁡x→03(1−cos⁡2x)xsin⁡x\lim_{x\to0}\frac{3\left(1-\cos^2x\right)}{x\sin x}x→0lim​xsinx3(1−cos2x)​ .

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Discover more resources for Mathematics

Evaluate $\lim_{x\to5}1$ .

Evaluate $\lim_{x\to1}5e^2-10\pi$ .

Evaluate $\lim_{x\to4}4x-1$ .

Evaluate $\lim_{x\rightarrow0}\ \left(3x-2\right)^4$ .

Evalulate $\lim_{x\to7}\frac{3x}{\sqrt{x+2}}$ .

Evaluate $\lim_{x\to0}\frac{\sqrt{x+2}-\sqrt{2}}{x}$ .

Evaluate $\lim_{x\to0}\frac{\sqrt{x^2}}{x}$ .

Evaluate $\lim_{x\to0}\frac{\sin^2x}{3x}$ .

Evaluate $\lim_{x\to0}\frac{\sec x}{x\csc x}$ .

Evaluate $\lim_{x\to0}\frac{3\left(1-\cos^2x\right)}{x\sin x}$ .