Quiz about Calculus

Question 1

Find the gradient of the tangent to $$y=\frac{x^3}{x^2-1}$$ at x = 2.

Accepted Answer

$$\frac{4}{9}$$

Answer

$$\frac{3}{5}$$

Answer

$$\frac{1}{3}$$

Answer

$$\frac{2}{9}$$

Question 2

Find the derivative of $$y=\log_2x+\log_3\left(x^3\right)$$

Accepted Answer

$$\frac{\ln24}{x\ln2\ln3}$$

Answer

$$\frac{1}{x\ln2}$$

Answer

$$\frac{\ln2}{x\ln2\ln3}$$

Answer

$$\frac{3}{x\ln3}$$

Question 3

Consider $$g\left(x\right)=3-2\cos2x$$ . Find $$g$$ .

Accepted Answer

4sin2x

Answer

4sinx

Answer

3sin2x

Answer

3sinx

Question 4

Inflexion points occur when the graph changes from concave down to concave up or vice versa.

Accepted Answer

true

Answer

false

Question 5

Let g(x) = -xcosx and find g'(x).

Accepted Answer

-cosx+xsinx

Answer

-cosx-xsinx

Answer

cosx-sinx

Answer

-cosx+sinx

Question 6

Consider the curves $$y=\sqrt[]{3x+1}$$ and $$y=\sqrt[]{5x-x^2}$$ . Find the point of intersection.

Accepted Answer

(1,2)

Answer

(1,3)

Answer

(3,5)

Answer

(3,1)

Question 7

Consider the curve $$y=\frac{a}{x}-x^2+1$$ . The gradient of the tangent to the curve is -5 when x = 2. Find the value of a.

Accepted Answer

4

Answer

1

Answer

3

Answer

5

Question 8

Find the gradient of the tangent to $$f\left(x\right)=\cos^4x$$ at the point where $$x=\frac{3\pi}{4}$$ .

Accepted Answer

1

Answer

4

Answer

3

Answer

0.5

Question 9

Find $$f$$ if $$f\left(t\right)=\frac{t+9}{e^t}$$ .

Accepted Answer

$$\frac{-t-8}{e^t}$$

Answer

$$\frac{-t+8}{e^t}$$

Answer

$$\frac{t+8}{e^t-8t}$$

Answer

$$\frac{-t-8}{8t-e^t}$$

Question 10

Given $$f\left(x\right)=e^{ax+2}+x^2$$ and $$f\left(2\right)=f$$ . Find a

Accepted Answer

1

Answer

1.5

Answer

3

Answer

2

Calculus

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