Hot questions in Calculus

+5 votes

4 answers

GATE2017-1-28
The value of $\lim_{x\rightarrow 1} \frac{x^{7}-2x^{5}+1}{x^{3}-3x^{2}+2}$ (A) is 0 (B) is -1 (C) is 1 (D) does not exist

asked Feb 14 in Calculus by Arjun Veteran (319k points) | 833 views

+2 votes

1 answer

UGCNET-Jan2017-II-3
The functions mapping R into R are defined as : $f(x)=x^{3}-4x, g(x)=\frac{1}{x^{2}+1}$ and $h(x)=x^{4}.$ Then find the value of the following composite functions : $h\circ g(x)$and $h\circ g\circ f(x)$ (1) (x2 + 1)4 and [(x3 – 4x)2 + 1]4 (2) (x2 + 1)4 and [(x3 – 4x)2 + 1]–4 (3) (x2 + 1)–4 and [(x2 – 4x)2 + 1]4 (4) (x2 + 1)–4 and [(x3 – 4x)2 + 1]–4

asked Oct 8 in Calculus by amaity Loyal (3.2k points) | 24 views

+1 vote

1 answer

integration question
$f(x) = \int_{- \infty}^{\infty} f(x) e^{2\pi x} dx$ solve f(x)

asked Oct 11 in Calculus by Pavan Kumar Munnam Veteran (10.6k points) | 68 views

+2 votes

1 answer

Integration doubt
Integrate the following- e^2 ∫ | loge x/x| dx e^-1

asked Oct 9 in Calculus by Surya Dhanraj Loyal (2.7k points) | 27 views

+2 votes

0 answers

Maxima and minima
Could we always say that in case of local minima or maxima we do not consider the extreme points we only check for critical points while in case of absolute maxima we check both at end points as well as at critical point...Please correct me if I am wrong.

asked Oct 8 in Calculus by shivangi5 Active (1k points) | 65 views

+2 votes

0 answers

Integration

asked Oct 8 in Calculus by shivangi5 Active (1k points) | 29 views

+1 vote

1 answer

Area Bounded By Curve
Let f(x)=x−(1/2) and A denote the area of region bounded by f(x) and the x-axis, when x varies from -1 to 1. A is nonzero and finite??

asked Sep 8 in Calculus by Shubhanshu Boss (9.1k points) | 63 views

+1 vote

1 answer

Integration doubt
1 0 [3x] dx

asked Oct 9 in Calculus by Surya Dhanraj Loyal (2.7k points) | 21 views

+1 vote

2 answers

Differential calculus
If f(x) = |x-1| + |x-2| is not derivable at x = (a) x = 0 (b) x = 1,2 (c) x = 3 (d) none

asked Sep 20 in Calculus by Dhanraj vishwakarma (265 points) | 47 views

+3 votes

3 answers

calculus problem on limits

asked Aug 8 in Calculus by Vicky rix Loyal (4.9k points) | 75 views

+9 votes

6 answers

GATE2015-2_26
Let $f(x)=x^{-(1/3)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from -1 to 1. Which of the following statements is/are TRUE? $f$ is continuous in [-1, 1] $f$ is not bounded in [-1, 1] $A$ is nonzero and finite II only III only II and III only I, II and III

asked Feb 12, 2015 in Calculus by jothee Veteran (92.7k points) | 1.8k views

0 votes

0 answers

anyone explain this limit question self made :P

asked Sep 18 in Calculus by sumit goyal 1 Loyal (3k points) | 66 views

+2 votes

0 answers

Limits
someone please explain how to solve these kind of questions. i am familiar with one variable and do not know how to solve for more than one variables

asked Sep 8 in Calculus by sandeepjkh Active (1.4k points) | 58 views

0 votes

1 answer

self doubt
Which of the following is true: (a) differentiable and continous (d) none of these (c) not differentiable but continous (b) neither differentiable nor continous

asked Sep 9 in Calculus by Kaluti Loyal (3.2k points) | 45 views

0 votes

0 answers

Maxima minima
Can a function obtain local maxima or minima at end point of its domain?

asked Sep 13 in Calculus by sachin! Active (1.6k points) | 30 views

0 votes

0 answers

Continuity
If the function f(x) = [(x-2)3/a] sin(x-2) + a cos(x-2) , [∙] denotes greatest integer function, is continuous & differentiable in (4,6) then find ‘a’ range? (A) a ϵ (-∞,∞) (B) a ϵ [64, ∞) (C) a ϵ [128, ∞) (D) Not defined

asked Sep 6 in Calculus by Sonu Kumar 1 (163 points) | 33 views

0 votes

0 answers

Continuity and Differentiability

asked Sep 6 in Calculus by Sonu Kumar 1 (163 points) | 31 views

0 votes

1 answer

limit
solve following $\lim_{x->0} e^{ax}- e^{-ax}/ log(1+bx)$

asked Aug 30 in Calculus by sid1221 Active (2.1k points) | 52 views

0 votes

0 answers

ME , GATE2006
Assuming $i=\sqrt{-1}$ and t is real number , $\int_{0}^{\Pi /3} e^{it}dt$ given ans is $\sqrt{3}/2 + i/2 , and i am getting \sqrt{3}/2-i/2$ i solved first put $e^{it}= cost +isint$ then and integrate , but in solution they first integrate $e^{it}$ then put the value of it ... but ans different ... why is this happening .. am i missing something ??

asked Aug 29 in Calculus by sid1221 Active (2.1k points) | 32 views

0 votes

1 answer

MATHS
Limit x tends to infinity then what is the value of (tanx-x)/(sinx)

asked Aug 21 in Calculus by tajar (85 points) | 60 views

+1 vote

0 answers

maxima minima problem
The greatest value of the function f(x) = 2 sin x + sin 2x on the interval [ 0,3pi/2 ] is ____ .

asked Aug 10 in Calculus by Vicky rix Loyal (4.9k points) | 102 views

+1 vote

2 answers

ISRO 2010-ECE Calculus
What does the following integral evaluate to? a) 5 π /16 b) 5 π /8 c) 0 d) 5 π /32

asked Feb 28 in Calculus by sh!va Veteran (30.2k points) | 76 views

+1 vote

1 answer

calculus problem on limits
1) 2) Answer for 1) infinity 2) 1/sqrt(3) please verify

asked Aug 8 in Calculus by Vicky rix Loyal (4.9k points) | 67 views

+1 vote

1 answer

doubt in calculus
What is the difference between monotonically increasing and strictly increasing ??? are they both same or different ???

asked Aug 5 in Calculus by Vicky rix Loyal (4.9k points) | 25 views

+1 vote

1 answer

Proof Results in Limits
Proof these results in limits 1. $\lim_{x\rightarrow0}(1+x)^{1/x} = e$ 2. $\lim_{x\rightarrow0}(1+nx)^{1/x} = e^n$ 3. $\lim_{x\rightarrow\infty }(1+\frac{1}{x})^{x} = e$ 4. $\lim_{x\rightarrow\infty }(1+\frac{a}{x})^{x} = e^a$

asked Jul 28 in Calculus by Shubhanshu Boss (9.1k points) | 47 views

+1 vote

1 answer

Calculus: Need Explanation
Q1> $\lim_{x->0} xlogx$ Q2> $\lim_{x\rightarrow Inf} \frac{sin x}{ x}$ for first question why we can't take: $\frac{x^{2} log x}{x}$

asked Jul 28 in Calculus by Shubhanshu Boss (9.1k points) | 39 views

+1 vote

0 answers

self doubt
compute the integral here $\int_{0}^{1} (x*logx)^{50}dx$

asked Jul 31 in Calculus by Kaluti Loyal (3.2k points) | 50 views

+1 vote

1 answer

Doubt in calculus
How to solve question 1 without reduction formula. Q1> $\int_{0}^{ \Pi /2}sin^6xcos^2xdx$ Q2> $\lim_{x\rightarrow0}\frac{1-cos^2}{2x^4}$

asked Jul 28 in Calculus by Shubhanshu Boss (9.1k points) | 38 views

+1 vote

0 answers

GATE 2015-2_26 Re-ask
Consider this question:- http://gateoverflow.in/8124/gate2015-2_26 Please clarify my doubts:- I have drawn its graph and I am getting an open graph without any bounded region. In this, the 2nd point says that f is not bounded in ... comparing with the graph I am getting infinite area since the area is not bounded. Then how the third point is true?

asked Jul 28 in Calculus by Shubhanshu Boss (9.1k points) | 41 views

+1 vote

0 answers

Maths
http://gateoverflow.in/?qa=blob&qa_blobid=3841640957822066036 Can someone show a step wise simplification for this

asked Jul 19 in Calculus by nick17india (63 points) | 40 views

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