Recently Active Calculus Questions

\lim_{z \rightarrow \infty}\frac{\int_{1/2}^{z}{[cot^{-1}x]dx}}{\int_{1/2}^{z}{[1+\frac{1}{x}}]dx} where [.] is GINT ...

i know this is not directly integrable, bt i'm nt getting any way to directly derive this relationship if \int_{0}^{1}{\frac{e^{t}}{t+1}} =a and \int_{3}^{4}{\frac{e^{t}}{t-5}} =b then find the relation btw a and b??? ...

k= \lim_{n\to\infty}\frac{(2n+1)\int_{0}^{1}x^{n-1}\sin\left(\frac{\pi}{2}x\right)dx}{(n+1)^{2}\int_{0}^{1}x^{n-1}\cos\left(\frac{\pi}{2}x\right)dx}\ \ (n=1,\ 2,\ \cdots). find k ...

evaluate !!!!!!!!!!!!!! 1. \int \frac{3x ^2 - 7 dx}{ (x^2 -4) ( x^2 + 1 ) } 2 . \int \frac{ dx}{ x.\sqrt{x^6 + 1} } 3. \int \frac{ \sqrt{x} dx}{(1+ x^2)^{\frac{7}{4}}} just practice problems [1] ...

INTEGER ANS TYPE QS 1) Let F (x) be a non- negative continuous function defined on R such that F (x) + F ( x+1/2) = 3 and the value of ∫[0--->1500] F(x)dx is 9000/a . Then the numerical value of ' a ' is . ...

INTEGER ANS TYPE 1) Let f(x) = 30 - 2x - x3 , then find the number of positive integral values of x which satisfies f ( f ( f ( x ) ) ) > f ( f ( -x ) ) . ...

Some might-be-too-easy-type integrals, i don't know exactly :P. *Image* ...

Q)→Assertion: Function f(x)=1/1-x is a continous function. Reason: A continous function is that which is continous in its domain with no breaks and hence in the function f(x)=1/1-x x=1 is not in the domain of this function. ...

If f(x) is continuous function and attains only rational values. If f(0) = 5, then roots of the equation (f(0))x2 + f((5))x + f(3) = 0, are 1. Real and equal 2.Real and unequal 3. Non-real complex cubic roots of unity 4. Irra ...

* GOT THE ANSWR ** ...

limx→π/2 (sinx - sinxsinx)/(1-sinx+lnsinx) ...

Q1) The function f : R → R defined by f(x)=x3+x2 is (a) one to one (b) onto (c) one to one and onto (d) neither one to one nor onto Q2) The function f(x)= x2/|x| if x is not = 0 = 0 if x=0 (a) is not continuous at x = 0 (b) ...

For any acute angled \Delta ABC find the minimum value of \frac{sinA}{A}+\frac{sinB}{B}+\frac{sinC}{C} ...

\int_{0}^{100\pi }{} (sin x)(e^{(\mid cos x\mid + \mid sin x\mid )})(log \mid sin x\mid ) dx is equal to A) 100 B)2 C) 0 D)50 \pi ...

sorry deleted the integral ...

\large \int_{0}^{\Pi /2}{\frac{dx}{9 + 16cos^{2}x}} ...

If f(x)=\frac{1-x}{1+x} , Then find f2010(x) = here f2010(x) = fofof................2010 times. ...

Consider the curve \mid y\mid = \mid x 2 - 4 \mid x\mid \mid A) Area bounded by curve is 128/3 sq.units. B) Area bounded by curve is 64/3 sq. units. C) Number of tangents drawn from (8,0) may be 4. D) Number of tangents drawn ...

*Image* ...

Q1 Find F(x)=limn→∞( x2nf(x)+g(x)/x2n+1 ) when: a)x<-1 b)-1<x<0 c)0<x<1 d)x>1 where f(x) and g(x) are continuous functions Q2 limn→∞ an/n! ; a ε R Q3 limn→∞ (1+ 1/a1 )(1+ 1/a2 )(1+ 1/a3 )...(1+ ...

Find f(x) which is a continuos fuction such that f(x)=\frac{e^{2x}}{2(e-1)}\int_{0}^{1}e^{-y}f(y)dy+\int_{0}^{\frac{1}{2}}f(y)dy+\int_{0}^{\frac{1}{2}}\sin^{2}(\pi y)dy for practice. ...

xy(d^2y/dx^2)+x(dy/dx)^2+y(dy/dx)=0 ...

IF f(x)=e-ln x and f(2m2 + m +1) < f(3m2 - 4m + 1) then m belongs to A. (0,5) B. (-7,-3) C. (3,17) D. none of these. ...

1..THE POSITIVE REAL FUNCTION SATISFIES F(X)/F(Y) ≤7(X-Y)2 FOR X , Y BELONG TO ITS DOMAIN ,F(3/2)= Π/4 THEN 1.F(X)= X +X3 2.F'(7)=0 3.F(X)=∫sin-1 t dt +∫ cois-1 t dt (in 3--limit for sin-1 t is from 0 to sin2x while fo ...

find : \ \int_{0}^{\pi}\frac{\cos nx}{2-\cos x}dx\ (n = 0,\ 1,\ 2,\ \cdots) ...

Q1 f:R→ R ;f(x) is continuous funciton satisfying f(x)+f(x2)=2 for all x ε R,the f(x) is a)into b)many one c)constatn d)periodic Q2 If [x] denotes GINT and f(x) =[n+p.sinx],0<x<π ,n ε I and p is a prime no., If p=1 ...

someone plzz see the miscelaaneous exercise on chapter8, q no.10, ncert for class XII.... the ans is wrong at the back of ncert...it ought to be 5/6 ...

Q1- A: if f(x) is discontinous at a point c and g(x) is continous at c and f(x).g(x) is continous at c then f(x) must be 0 at point c. B: if f(x) and g(x) are two continous function in their domain then f(x).g(x) must be cont ...

\int_{0}^{2\pi }{e^{\cos \theta }cos(sin\theta )d\theta }= ...

(1) Lim \frac{n}{10^{n+1}}= n-->∞ ...