`x^2+1/(x^2)=79 ,f i n d t h e v a l u e o fx+1/x`

IfI_n=int_x^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

If f(0)=1,f(2)=3,f(2)=5,t h e nfin dt h ev a l u eof int_0^1xf"(2x)dx

I fx+1/x=2,t h e p r i n c i p a l v a l u e o f sin^(-1)x is

f(x)=int_1^x(tan^(-1)(t))/t dtAAx in R^+,t h e nfin dt h ev a l u eof f(e^2)-f(1/(e^2))

Iff(x)=x+int_0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is equal to _________

: If f(x)={x^2+2,xgeq2 1-x ,x 1, 3-x , xlt=0,t h e nt h ev a l u eoflim_(x->1)f(g(x))i s__

If int1/(x+x^5)dx=f(x)+c ,t h e ne v a l u a t eint(x^4)/(x+x^5)dxdot

If int1/(x+x^5)dx=f(x)+c ,t h e ne v a l u a t eint(x^4)/(x+x^5)dxdot

I ff(x)=2tan^(- 1)x+sin^(- 1)((2x)/(1+x^2)), x > 1 .T h e n , f(5) is equal to

(i) Let h (x) = underset(x to oo)lim(x^(2n) f(x) + g(x))/(1+x^(2n)) , find h(x) in terms of f(fx) and g(x) (ii) without using L Hospital rule or series expansion for e^(x) evaluate underset(x to 0) lim (e^(x) -1-x)/x^(2) (iii) underset(n to oo) lim [ e^(1/n)/n^(2) + 2 ((e^(1/n))^(2))/n^(2) + 3. ((e^(1/n))^(3))/n^(2)+.......+ n((e^(1/n))^(n))/n^(2)] (iv) underset(x to 0)lim[ (a sin x)/x ] + [ (b tan x)/x] Where a,b are inegers and [] denotes integral part. (v) underset(x to a)lim (sinx/sina)^(1/(x-a))