f is a continous function in `[a, b]`; g is a continuous function in [b,c]. A function h(x) is defined as `h(x)=f(x) for x in [a,b) , g(x) for x in (b,c]` if f(b) =g(b) then

f is a continuous function in [a,b]; g is a continuous function in [b,c]. A function h(x) is defined as h(x)=f(x) for xϵ[a,b) =g(x) for xϵ(b,c]. If f(b)=g(b), then

Q.Let f:[a,b]rarr[1,oo) be a continuous function and let g:R rarr R be defined as g(x)={0 if x b

If a function f(x) defined by is continous on R, then (a , b) =

If a twice differentiable function f(x) on (a,b) and continuous on [a, b] is such that f''(x)lt0 for all x in (a,b) then for any c in (a,b),(f(c)-f(a))/(f(b)-f(c))gt

if f(x) and g(x) are continuous functions, fog is identity function, g'(b) = 5 and g(b) = a then f'(a) is

if f(x) and g(x) are continuous functions, fog is identity function, g'(b) = 5 and g(b) = a then f'(a) is

If a function f(x) satisfies f'(x)=g(x) . Then, the value of int_(a)^(b)f(x)g(x)dx is

If f(x)a n dg(x) are continuous functions in [a , b] and are differentiable in (a , b) then prove that there exists at least one c in (a , b) for which. |f(a)f(b)g(a)g(b)|=(b-a)|f(a)f^(prime)(c)g(a)g^(prime)(c)|, w h e r e a