Quiz about NEJA GROUP

Question 1

y=f(x) is the solution for $$\frac{ ext{d}y}{ ext{d}x}=ky\ $$ find f(x) if k is a constant

(no calculator)

Accepted Answer

$$2e^{\frac{x}{5}\ln15}$$

Answer

$$\frac{28x}{5}+2$$

Answer

$$2e^{\frac{x\left(\ln28\right)}{5}}$$

Answer

$$\frac{x^2}{25}+\frac{27x}{5}+2$$

Question 2

Which of the following is true?

$$I\lim_{x\rightarrow-5^+}f\left(x\right)\ =\ \inf\ $$

$$II\lim_{x\rightarrow0}f\left(x\right)\ =\ -1$$

$$III\lim_{x\rightarrow-5^-}f\left(x\right)\ =\ \inf$$

Accepted Answer

$$I\ and\ III\ only$$

Answer

$$I$$ only

Answer

$$I\ and\ II$$ only

Answer

$$I,\ II\ and\ III$$

Question 3

If $$f\left(x\right)\ =\ \int_3^{x^2}\frac{1}{\cos x}dx\ \ for\ x\ge3,\ then\ f$$

Accepted Answer

$$\frac{2\pi}{\cos\left(\pi^2\right)}$$

Answer

$$\frac{1}{\cos\pi}$$

Answer

$$\frac{\pi^2}{\cos^2\pi}$$

Answer

$$\frac{\pi^2}{\cos\left(\pi^2\right)}$$

Question 4

Find the value for f(2.6), given that f is differentiable and f(2) = 5 and f'(2) = 7 using approximation with the tangent line to the graph of f at x=2.

Accepted Answer

9.2

Answer

10.0

Answer

9.7

Answer

9.0

Question 5

Evaluate
$$\lim_{x ightarrow\ \frac{\pi}{2}}\ \frac{\left(x-\frac{\pi}{2} ight)}{x} an x$$

Accepted Answer

$$-\frac{2}{\pi}$$

Answer

$$\frac{2}{\pi}$$

Answer

$$1-\frac{2}{\pi}$$

Answer

$$2+\frac{\pi}{2}$$

Question 6

As x in the function $$\frac{3x^2+2x}{\sqrt[2]{16x^4+25x}}$$ approaches positive infinity, what is the limit?

Accepted Answer

3/4

Answer

3/16

Answer

9/16

Answer

Does Not Exist

Question 7

$$y\ =\ 5e^{2x\ }+2$$

Provided the equation above, which of the following equations is true?

Accepted Answer

$$y^4\ -\ 4y$$

Answer

2y'' - 20e^(2x) - 2 = 0

Answer

y' + y''' - 20e^(2x) + 10e^(2x) = 0

Answer

$$\left(y^4\right)\left(y$$

Question 8

The region R is bounded by $$y\ =\ e^{-x}\ +\ 2$$ , x = 3, the y-axis, and y = 2 is revolved about the line y = 1. Which of the following definite integral would find the volume of this solid after its revolution?

Accepted Answer

$$-\pi\int_0^31\ dx\ +\ \pi\int_0^3\ \left(e^{-x}\ +1\right)^2\ dx$$

Answer

$$-\pi\int_0^3\ \ \left(1^2\right)\ dy\ +\ \pi\int_0^3\ \left(e^{-x}\ +\ 2\right)^2\ dy$$

Answer

$$-\pi\int_0^3\ \left(1^2\right)\ dx\ +\ \pi\int_0^3\left(e^{-x}+2\right)^2dx$$

Answer

$$-\pi\int_0^3\ 1\ dx\ +\ \pi\int_0^3\ \left(e^{-x}\ +1\right)\ dx$$

Question 9

Let f and g be inverse functions.

The following tbale lists a few values of f, g, and g'.

Determine f'(5).

Accepted Answer

None of the above

Answer

0

Answer

4

Answer

1/4

Question 10

The graph of y=f'(x) is shown above. Which of the following could be the graph of y=f(x)?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

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