limits exerise

answer for 2.)d.) I got is e and i need to get it approved so if anyone please!!!!!

2.)a.) apply L'hospital and then bring x⁵ out of the fifth root in the denominator you will get the answer to be 1!!!!!!!!

1.)c.) see reply no#1 from mirka!!!!!

1.)b.)
use the property 2 of the definite integrals and change the limits of the questions as:
limx--->0 -x\int_{1}^{x}{(cost)/t^2}
now apply L'Hospital and you will get it as:

hence i got the answer as 1

1.) a.) in the first step apply L'Hospital and then as follows:

so the answer that i got is 2

1 d i din get d final ans if sum1 get plz tell

Q2 (b) -

EDIT :
Step 3 is becoz wen u have limit of d form

lim x-> a { f(x) }^g(x)
where lim x->a f(x) = 1 and lim x ->a g(x) = ∞,

u can write d limit as
lim x-> a e^{(f(x) – 1)g(x)}

[1]

is d answer for Q1 . (c) = 2/3 ???

Q2 (C)

i have used L-Hopital rule, nd Leibnitz differentiation under integral sign

even me gt 2nd d e

@#6
Mirka
how can u say that limx-->0 x^x=1 [7][7]

Q2 (C) = 1/2 ?

And is answer to Q2 (b) = e ??

Q1 (b)limit does not exist finitely