" 4."sqrt((1-x)/(1+x))

lim_(x rarr 1) (4-sqrt(15+x))/(1-x)= ______.

If y = tan^(-1) ((4sqrt(x))/(1 - 4x))" then" (dy)/(dx) is

Differentiate tan^-1((4sqrt(x))/(1-4x))

Differentiate tan^-1((4sqrt(x))/(1-4x))

Using a suitable substitution,find the derivative of tan ^(-1)((4sqrt(x))/(1-4x)) with respect to x.

Let f(x)=-4.sqrt(e^(1-x))+1+x+(x^(2))/(2)+(x^(3))/(3) . If g(x) is inverse of f(x) then the value of (1)/(g^(')(-(7)/(6))) is

Let f(x)=-4.sqrt(e^(1-x))+1+x+(x^(2))/(2)+(x^(3))/(3) . If g(x) is inverse of f(x) then the value of (1)/(g^(')(-(7)/(6))) is

Discuss the continuity of f(x) = 0 at x = 0 if f(x) = {{:((sqrt(1 + 4x)- sqrt(1 - 4x))/(sin x)"," ,x != 0),(4, x = 0):}

If f(x) is continuous at x=0 , where f(x)={((sin x)/(x)+cos x", for " x gt 0),((4(1-sqrt(1-x)))/(x)", for " x lt 0):} , then f(0)=

Prove that : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=pi/4-1/2cos^(-1)x,-1/sqrt2lexle1