So that `x^5+x+1=0` for some value of x between -1 and 0.

Prove that e^x-2=0 has a solution between 0 and 1.

IF the derivative of tan ^(-1)(a + bx) w.r.t.x takes the value 1 at x= 0, write the relationship between a and b.

Show that (x^(5) - 5x^(4) + 5x^(3) - 1) has local maximum value when x = 1, a local minimum value when x = 3 and neither when x = 0.

Write the value of df, if f(x) = ln (1 + x), x = 1 and &x=0.04.

What is the value of delta y, if y = x^2 - 1 , x=1 and delta x = 0.02?

what is the value of int_0^(1) x(1-x)^99 dx ?

If f(x) = {((1-cos4x)/x^2, when x 0):} . is continuous at x=0, then the value of a will be.

The function f(x) = {[6.5, for x le 0],[2a + x, forx>0]:} continuous at x = 0. Then what is value of a ?

If [{:(3,2),(7,x):}][{:(5,-2),(-7,y):}]=[{:(1,0),(0,1):}] then find the value of x and y .

If a function f(x) is defined by f(x) = {((1+7x)^(1/x),when x!=0),(k,when x =0):} is continuous at x = 0, then what is the value of k.?