Free Printable 4th Quarter Basic Calculus

1.

1. A function f(x) is continuous when all of the following are satisfied except

a)

limit of f(x) exists

b)

f(x) is defined

c)

f(x) is removable

d)

limit of F(x) = f(a)

2.

$\ What\ is\ the\ derivative\ of\ x^4+3x^3+1$

a)

$4x^3+9x^2+1$

b)

$4x^2+9x$

c)

$4x^3+9x^2$

d)

$4x^2+9x$

3.

$Find\ the\ derivative\ of\ x^{4\ }+3x^3-5x$

a)

$4x^3+9x^2-5$

b)

$4x^3+9x^2$

c)

$4x^2+9x$

d)

$4x^2+5$

4.

$Find\ derivative\ of\ (𝑥+1)^2$

a)

$x+1$

b)

$2\left(x+1\right)$

c)

$2x$

d)

$2x\left(x+1\right)$

5.

Find derivative of $\sin(2𝑥)$

a)

$−2\sin(2𝑥)$

b)

$2\cos(2𝑥)$

c)

$2\cos𝑥\sin x$

d)

$−2\cos𝑥\sin x$

6.

find derivative of $\sin^2\ x$

a)

$2\cos(2𝑥)$

b)

$2\cos𝑥\sin x$

c)

$−2\sin(2𝑥)$

d)

$−2\cos𝑥\sin x$

7.

Find the derivative of

$\frac{d}{dx}\tan x$

a)

$\operatorname{cosec}x\cot x$

b)

$\sec x\ \tan x\$

c)

$\sec2x$

d)

$-\operatorname{cosec}x\cot x\$

8.

Find the derivative of

$\frac{d}{dx}\cos x$

a)

$\sin x$

b)

$-\sin x$

c)

$-\operatorname{cosec}x\cot x$

d)

$\sec2x$

9.

What is the derivative of y = 2π ?

a)

0

b)

2

c)

-2

d)

None of the above

10.

In what value of x will the following function discontinuous?

a)

-1

b)

-2

c)

-3

d)

-4

11.

Which of the following best describes the continuity at x = 2?

a)

Jump Discontinuity

b)

Removable Discontinuity

c)

Continuous

d)

Infinite Discontinuity

12.

At which x-value is there a jump discontinuity?

a)

$x=-3$

b)

$x=-6$

c)

$x=1$

d)

$x=2$

13.

Which of the following best describes the continuity at x = -4?

a)

Continuous

b)

Removable Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

14.

Is the function continuous at x = 2, and why?

a)

Yes, $\lim_{x\rightarrow2}f\left(x\right)=f\left(2\right)$

b)

Yes, $\lim_{x\rightarrow2^-}f\left(x\right)=\lim_{x\rightarrow2^+}f\left(x\right)$

c)

No, $\lim_{x\rightarrow2^-}f\left(x\right)\ne\lim_{x\rightarrow2^+}f\left(x\right)$

d)

No, $\lim_{x\rightarrow2}f\left(x\right)\ne f\left(2\right)$

15.

Which of the following best describes the continuity at x = 3?

a)

Continuous

b)

Removable Point Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

16.

Find the derivative of f(x)=(x³-2x)²

a)

(x³- 2x) (3x²)

b)

2x²(x³- 2x)

c)

6x²(x³- 2x)

d)

3x³(x³- 2x)

17.

Find dy/dx for y=-(3x²+5x)⁵

a)

y=-5(x+5)⁴

b)

y=-5(6x+5)(3x²+5x)⁴

c)

y=-6x+5(3x²+5x)⁴

d)

y=-6x(3x²+5x)⁴

18.

the derivative is...

a)

slope of the secant line

b)

slope of the tangent line

c)

slope of the cosecant line

d)

slope of the normal line

19.

Let f be the function defined below. What is the exact value of the slope of an equation of the line tangent to the graph of f(x) at the point where x = -1?

f\left(x\right)=4x^3-5x+3

a)

y' = -7

b)

y'= 7

c)

y' = 17

d)

y'= -17

20.

The distance between A(3,1) and B(-2,-1) written correctly is:

a)

$\sqrt{\left(-2-3\right)^2\ +\ \left(-1-1\right)^2}$

b)

$\sqrt{\left(1-3\right)^2\ +\ \left(-1-2\right)^2}$

c)

$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$

d)

$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$

21.

Find the distance between ( 1, 3) and (5, 6)

a)

3

b)

4

c)

5

d)

6

22.

$𝑥^2−2$

a)

$2x-2$

b)

$2$

c)

$2x$

23.

in what value of x does the following function is discontinuous?

a)

3

b)

-3

c)

6

d)

-6

24.

Use the definition of continuity to determine whether the function is continuous at x = 7.

a)

Yes, it's continuous at x = 7.

b)

No, it's not continuous because the function is not defined at x = 7.

c)

No, it's not continuous because the limit does not exist as x approaches 7.

d)

No, it's not continuous because the value at x = 7 does not equal the limit.

25.

Over which interval is the function continuous?

a)

[-6, -1]

b)

[-1, 1]

c)

[1, 6]

d)

None of the Above

4th Quarter Basic Calculus

Total questions: 25

Worksheet time: 23mins

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