c) If `f(x) =7^x` then prove that, `f(m+n+p) = f(m). f(n). f(p)`

If f (x) = cot x, then prove that : f(-x)=-f(x)

If f(x) = alphax^(n) prove that alpha = (f'(1))/n

If f(x)=alphax^n , prove that alpha=(f^(prime)(1))/n .

if f(x) = x^n then the value of f(1) - (f'(1))/(1!) + (f''(1))/(2!) + ---+((-1)^n f''^--n times (1))/(n!)

If f(x) is polynomaial function of degree n, prove that int e^x f(x) dx=e^x[f(x)-f'(x)+f''(x)-f'''(x)+......+(-1)^n f^n (x)] where f^n(x)=(d^nf)/(dx^n)

If f_1(x)=x ,f_2(x)=1-x ,f_3(x)=1/x ,f_4(x)=1/(1-x),f_5(x)=x/(x-x),f_5(x)=x/(x-1), , f_6(x)=(x-1)/x suppose that f_6(f_m(x))=f_4(x) and f_n(f_4(x))=f_3(x), then m=5 (b) n=5 (c) m=6 (d) n=6

A function f is said to be periodic if it repeats its nature after certain interval and that interval is called period of the function. If T be the period of f(x), then f(x + T) = f(x). For example f(x) = tan x is periodic with period pi . Then find the period of f(x) that satisfies the following condition. (i) f(x + 1) - f(x + 3) = 0 (ii) f(x + 3) + f(x) = 0 (iii) f(x-1) + f(x+3) = f(x+1) + f(x + 5) (iv) f(x + p) = 1+{(1-f(x-p))^(2n+1)}^((1)/(2n+1)), n in N

If f (x) is a function such that f(x+y)=f(x)+f(y) and f(1)=7" then "underset(r=1)overset(n)sum f(r) is equal to :

If f(x)=(1+x)^2, then the value of f(x0)+f^(prime)(0) +(f^(0))/(2!)+(f^(0))/(3!)+(f^n(0))/(n !)dot

If f(x)=(1+x)^2, then the value of f(x0)+f^(prime)(0) +(f^(0))/(2!)+(f^(0))/(3!)+(f^n(0))/(n !)dot