Let `h(x)=x^(m/n)` for `x in R ,` where m and n are odd numbers where 0`<`m`<`n. Then y= h(x) has a. no local extremums b. one local maximum c. one local minimum d. none of these

Let f(x)=[n+p sin x], x in (0, pi) n in Z and p is a prime number, where [.] denotes the greatest integer function. Then find the number of points where f(x) is not differentiable.

Let f(x)=e^({e^(|x|sgnx)})a n dg(x)=e^([e^(|x|sgnx)]),x in R , where { } and [ ] denote the fractional and integral part functions, respectively. Also, h(x)=ln(f(x))+ln(g(x)) . Then for real x , h(x) is

Consider a point A(m,n) , where m and n are positve intergers. B is the reflection of A in the line y=x , C is the reflaction of B in the y axis, D is the reflection of C in the x axis and E is the reflection of D is the y axis. The area of the pentagon ABCDE is a. 2m (m+n) b. m (m+3n) c. m(2m+3n) d. 2m(m+3n)

Prove that the function f(x)= x^(n) is continuous at x= n, where n is a positive integer.

In the expansion of (1+x)^(m+n) , where m & n are +ve integers, prove that the coefficients of x^m and x^n are equal.

What is the zero of the polynomial p(x)=(x^(n)-1)/(2^(x)-1) , where n is a natural number and xne0 ?

If f(x)=(a-x^n)^(1/n)," where "a gt0 and n is a positive integer, show that f[f(x)]=x.

Prove that (1+x)^(n) ge (1+nx) for all natural number n where x gt -1

(1+x)^n-nx-1 is divisible by (where n in N)