In the mean value theorem, `f(a+h)=f(a)+hf'(a+theta h) (0 lt theta lt 1),` find `theta` when `f(x)=sqrt(x), a=1 ` and `h=3. `

In the mean value theorem f(a+h)=f(a)+hf'(a+theta h) ( 0 lt theta lt 1) , if f(x)=sqrt(x), a=1, h=3 , then the value of theta is -

In the mean value theorem, f(x+h)=f(x)+hf'(x+theta h)(0 lt theta lt 1), if f(x)=e^(x) , then show that the value of theta is independent of x.

In the following Lagrange's mean value theorem, f(a+h)-f(a)=hf'(a+theta h), 0 lt theta lt 1 If f(x)=(1)/(3) x^(3)-(3)/(2) x^(2)+2x, a=0 and h=3 " find " theta .

If f(x+h) =f(x)+hf'(x+theta h) , find theta , given x=-a, h=2a and f(x) =root(3)(x) .

In the mean value theorem f(b)-f(a)=(b-a)f'(c ), (a lt c lt b)," if " f(x)=x^(3)-3x-1 and a=-(11)/(7), b=(13)/(7) , find the value of c.

If 0^@ lt theta lt 90^@ , find theta when 2 cos theta+2sqrt2=3sec theta

Lagrange's mean value theorem is , f(b)-f(a)=(b-a)f'(c ), a lt c lt b if f(x)=sqrt(x) and a=4, b=9, find c.

Applying Lagrange's mean value theorem for a suitable function f(x) in [0, h], we have f(h)=f(0)+hf'(thetah),0 lt theta lt1 . Then for f(x)=cosx , the value of underset(h to0+)lim theta is-

If sqrt(3) sin theta - cos theta = 0 and 0^(@) lt theta lt 90^(@) , find the value of theta .

If f(x)=(1)/(x) , then find the value of theta in the mean value theorem f(x+h)=f(x)+hf'(x+theta h), 0 lt theta lt 1 .