Let f(x)=e^{-\frac{1}{x^{2}}}+\int_{0}^{\frac{\pi x}{2}} \sqrt{1+\sin t} d t \forall x \in(0, \infty) then-

f' exists and is continuous \forall x \in(0, \infty)

f" exists \forall x \in(0, \infty)

There exists \alpha>0 such that |f(x)|>| {f}^{'}( {x})| \forall x \in(\alpha, \infty)

0 such that |f(x)|>| {f}^{'}( {x})| \forall x \in(\alpha, \infty) Solution: f^{'}(x)=e^{-\frac{1}{x^{2}}} \cdot \frac{2}{x^{3}}+\frac{\pi}{2} \sqrt{1+\sin \frac{\pi x}{2}} \lim_{x \to 0^{+}} {e^{-{1}/{x^{2}}}}/{x^{3}}=0 Also \lim_{x \to \infty} f(x)=\infty f^{' '}(x) does not exist for x=3,7,11 . . ." >

NEET Biology Complete Course by Moniba Madam - Watch Full Playlist

Test Index

JEE Advanced 2020 Full Test 5 Paper 2

Question : 45

Total: 54

Let f(x)=e−‌

∫

‌

πx

√1+sin‌tdt‌∀x∈(0,∞) then-

f' exists and is continuous ∀x∈(0,∞)
f" exists ∀x∈(0,∞)
f ' is bounded
There exists α>0 such that |f(x)|>|f′(x)|∀x∈(α,∞)

Validate

Go to Question:

Prev Question

Next Question

More Free Exams:

AIEEE Previous Papers
BITSAT Exam Previous Papers
JEE Advanced Chapters Wise Questions
JEE Advanced Previous Papers
JEE Mains Chapters Wise Previous Papers
JEE Mains Model Papers
JEE Mains Previous Papers
VITEEE Previous Papers