Limits

MCQs BCA II Semester
Topic: Limits

By Shankar Gyawali

Multiple Choice

Which of the following is not an indeterminate form?

• $$1^{\infty\ }$$

• $$\infty-\infty\$$

• $$\infty+\infty\$$

• $$\frac{0}{0}$$

Multiple Choice

$$\lim_{x\rightarrow a\ }\ \frac{\ x^n-a^n}{x-a}is\ equal\ to$$

• $$na^{n-1}$$

• $$na^{n+1}$$

• $$n^2a^{n-1}$$

• $$a^{n-1}$$

Multiple Choice

$$\lim_{x\rightarrow\infty\ }\ \frac{\ 3x^{2\ }+4x-1}{4x^2+5}\ is\ equal\ to$$

• $$\frac{1}{4}$$

• $$\frac{3}{4}$$

•  $$\frac{\ 5}{3}$$

•  $$\frac{4}{3}$$

Multiple Choice

$$\lim_{t\rightarrow1}\ \frac{4}{t-9}\ is\ equal\ to$$

• $$2$$

• $$-2$$

• $$\frac{1}{2}$$

• $$-\frac{1}{2}$$

Multiple Choice

$$\lim_{x\rightarrow0}\frac{\log_e\left(1+x\right)}{3x}\ is$$

• $$\frac{1}{3}$$

•  $$0$$

• $$\infty\$$

• $$3$$

Multiple Choice

$$\lim_{x\rightarrow0}\ \frac{\sin x\degree\ \ \ }{x}\ is\ equal\ to$$

• $$1$$

• $$\frac{\pi}{180}$$

• $$\frac{180}{\pi\ }$$

• $$0$$

Multiple Choice

$$\lim_{x\rightarrow0}\ \sin\left(\frac{1}{x}\right)$$

• $$0$$

• $$\infty$$

• $$1$$

• $$does\ not\ exist$$

Multiple Choice

$$\lim_{x\rightarrow0}\cos\ x$$  

• 0
  

• 1

• -1

• DNE

Multiple Choice

$$\lim_{x\rightarrow0}\ \frac{\cos x}{x}$$  

• 0

• 1

• -1

• DNE

Multiple Choice

$$\lim_{x\rightarrow0}\ \frac{\tan x}{x}$$  

• 0

• 1

• -1

• DNE

Multiple Choice

$$\lim_{x\rightarrow\infty}\ \frac{\sin x}{x}$$  

• 0

• 1

• -1

• DNE

Fill in the Blank

Find $$\lim_{\theta\rightarrow0}\ \frac{\theta}{\sin\theta}$$  

Multiple Choice

$$\lim_{x\rightarrow\ -\ \infty}\ 10^x$$  

• $$0$$  

• $$\infty$$  

• $$-\ \infty$$  

• $$DNE$$

Fill in the Blank

EXPONENTIAL FUNCTIONS

$$y=e^x$$  and  $$y=10^x$$  

both pass through point $$\left(a,b\right)$$  

Submit  $$a,b$$  

,

Multiple Choice

Find the limit of the function as x approaches 4 from the right.

• -1
• 2
• -2
• DNE

Multiple Choice

What is the limit of the function as x approaches 1 from the left?

• DNE
• 1
• 4
• -2

Multiple Choice

Find the limit of the function as x approaches 2⁺.

• 1
• -1
• 5
• DNE

Multiple Choice

$$\lim_{x\rightarrow4}-\ f(x)\ is\ equal\ to$$

• 3

• −4

• ∞

• dne

Multiple Choice

From the figure alongside what is the value of $$\lim_{x\rightarrow2}\ f\left(x\right)$$

• 0

• ∞

• - ∞

• does not exist