Let f:(a, b) → R be a differentiable function. Which of the follo…

MCQ

Let f:(a, b) → R be a differentiable function. Which of the following statements is true:

A
$ \displaystyle \lim_{\text{x} \rightarrow \text{a}}\text{f(x)}=\infty \Longrightarrow \lim_{\text{x} \rightarrow \text{a}} |\text{f(x)}|=∞$
B
$ \displaystyle \lim_{\text{x} \rightarrow \text{a}}\text{f(y)}=\infty \Longrightarrow \lim_{\text{x} \rightarrow \text{a}} |\text{f(y)}|=∞$
C
$ \displaystyle \lim_{\text{x} \rightarrow \text{a}}\text{f(y)}=\infty \Longrightarrow \lim_{\text{x} \rightarrow \text{a}} |\text{f(y)}|=∞\pi$
D
$ \displaystyle \lim_{\text{b} \rightarrow \text{a}}\text{f(y)}=\infty \Longrightarrow \lim_{\text{x} \rightarrow \text{a}} |\text{f(y)}|=∞\pi$

✓

Answer

$ \displaystyle \lim_{\text{x} \rightarrow \text{a}}\text{f(x)}=\infty \Longrightarrow \lim_{\text{x} \rightarrow \text{a}} |\text{f(x)}|=∞$'

Solution:

f : (a, b) → R is differentiable.

If $ \lim _\limits{ \text{x}\rightarrow \text{a} }{ \text{f}(\text{x} )}$

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