If f(x)=(lim)(nvecoo)(cos(x/(sqrt(n))))^...

If `f(x)=(lim)_(nvecoo)(cos(x/(sqrt(n))))^n` , then the value of `(lim)(xvec0)(f(x)-1)/x` is `0` b. `1` c. 2 d. `3//2`

Text Solution

AI Generated Solution

Topper's Solved these Questions

DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS
CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos
LINEAR INEQUALITIES
CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If f(x)=lim_(nrarroo) (cos(x)/(sqrtn))^(n) , then the value of lim_(xrarr0) (f(x)-1)/(x) is

If f(x)=lim_(m->oo) lim_(n->oo)cos^(2m) n!pix then the range of f(x) is

Evaluate: ("lim")_(xvec0)(x2^x-x)/(1-cosx)

Evaluate: ("lim")_(xvec0)(e^x^2-cosx)/(x^2)

The value of (lim)_(xvec0)(e^(2x)-cosx-ln(1+2x))/(xtanx-sinx)i s 0 (b) 1 (c) 2 (d) 3

Evaluate: ("lim")_(xvec0)(cot2x-cos e c2x)/x

If 3-((x^2)/(12))lt=f(x)lt=3+((x^3)/9) for all x!=0, then find the value of ("lim")_(xvec0)f(x)

Evaluate: ("lim")_(xvec0)(2^x-1)/(sqrt(1+x)-1)

If L=("lim")_(nvecoo)(2x3^2x2^3x3^4 x2^(n-1)x3^n)^1/((n^(2+1)) , then the value of L^4 is

If lim_(x->0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(lim_(x->0)[1+(f(x))/x]^(1/x))i s____

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions

The value of (lim)(xvec3)((x^3+27)(log)e(x-2))/(x^2-9) is a. 9 b. 1...
Text Solution
|
If (lim)(xvec0)(e^(a x)-e^x-x)/(x^2)=b (finite), then a=2,b=0 b. a=0,b...
Text Solution
|
If underset(xrarr0)(lim)(x^3)/(sqrt(a+x)(bx-sinx))=1,agt0, then a+b is...
Text Solution
|
underset(xrarr0)(lim)[(sin^(-1)x)/(tan^(-1)x)]= (where [.] denotes the...
Text Solution
|
The value of lim(x->pi/4) (sqrt(1-sqrt(sin2x)))/(pi-4x) is
Text Solution
|
lim(x->0) (sin x /x)
Text Solution
|
If f(x)=x((e^(|x|+[x])-2)/(|x|+[x])) then (where [.] represents the gr...
Text Solution
|
If A=underset(xrarr0)(lim)(sin^(-1)(sinx))/(cos^(-1)(cosx))and B=under...
Text Solution
|
Let f(x)=lim(m->oo){lim(n->oo)cos^(2m)(n !pix)}, where x in Rdot Then...
Text Solution
|
lim(x->oo ){(e^x+pi^x)^(1/x)}= where {.} denotes the fractional par...
Text Solution
|
Let f(x)=(lim)(xvecoo)(tan^(-1)(tanx))/(1+((log)e x)^n),x!=(2n+1)pi/2 ...
Text Solution
|
Assume that underset(thetararr-1)(lim)f(theta) exists and (theta^(2)+t...
Text Solution
|
lim(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)
Text Solution
|
Let f: RvecR be such that f(a)=1,f^(prime)(a)=2. Then (lim)(xvec0)((...
Text Solution
|
lim(x->oo)(1-x+x.e^(1/n))^n
Text Solution
|
If f(n)=underset(xto0)lim{(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"s...
Text Solution
|
If a >0,b >0 then (lim)(n->oo)((a-1+b^(1/n))/a)^n= b^(1//a) b. a^...
Text Solution
|
(lim)(xvec-pi/2 )[1+(cos x)^(cos x)]^2=
Text Solution
|
(lim)(xvec0)("log"(e^x^2+2sqrt(x)))/(t a nsqrt(x)) is equal to 0 b. 1 ...
Text Solution
|
If f(x)=(lim)(nvecoo)(cos(x/(sqrt(n))))^n , then the value of (lim)(xv...
Text Solution
|