Limit, Continuity and Differentiability · Mathematics · NDA

Consider the following statements :1. $f(x)$ is increasing in the interval $(e, \infty)$2. $f(x)$ is decreasing in the interval $(1, e)$3. $9 \ln 7 > ...

What is $\lim\limits_{x \to 0-} h(x) + \lim\limits_{x \to 0+} h(x)$ equal to?

What is f(0.5) equal to ?

What is $\displaystyle \lim _{x \rightarrow 1} \frac{f(x)-1}{g(x)}$ equal to?

What is $\displaystyle \lim _{x \rightarrow 1} f(x)^{\frac{1}{g(x)}}$ equal to?

What is $\displaystyle \lim _{x \rightarrow 0+}$ h(x) equal to ?

What is $\displaystyle \lim _{x \rightarrow 0-}$ h(x) equal to ?

What is the value of a ?

What is the value of b?

If the function f(x) is differentiable at x = 1, then what is the value of (a + b)?

What is $\displaystyle \lim _{x \rightarrow 0} $ f(x) equal to ?

What is $\lim _{x \rightarrow 0} \frac{f(x)}{x}$ equal to ? 

What is $\lim _{x \rightarrow 0} \frac{f(x)}{x^2}$ equal to ? 

What is the value of p ?

What is the value of q ?  

What is $\lim\limits_{x \rightarrow 5} \frac{5-x}{|x-5|}$ equal to ?

What is $\lim\limits_{x \rightarrow 1} \frac{x^9-1}{x^3-1}$ equal to ?

What is $\displaystyle\lim_{x \rightarrow 0} \frac{x}{\sqrt{1−\cos 4x}}$ equal to ?

What is $\displaystyle\lim_{x\rightarrow \frac{\pi}{2}} \frac{4x−2\pi}{\cos x}$ equal to ?...

If f(x) = $\frac{x^2+x+|x|}{x}$, then what is $\displaystyle\lim_{x \rightarrow 0}$ f(x) equal to ?...

What is $\displaystyle\lim_{h \rightarrow 0} \frac{\sin^2(x+h)−\sin^2x}{h}$ equal to ?...

Let y = [x + 1], -4 < x < -3 where [.] is the greatest integer function. What is the derivative of y with respect to x at x = -3.5?

What is $\lim\limits_{x \to 0}x^3(\text{cosec} \ x)^2$ equal to ?

What is $\lim\limits_{x \to 1}\frac{x^3 - 1}{\sqrt x - 1}$ equal to?