Calculus Answers

differentiate y=sin^-1 [2x-1]

The function f : x ı→ a + b cos x, is defined for 0 ≤ x ≤ 2π. Given that f(0) = 10 and that = 1 , find

(i) the values of a and b, (ii) the range of f, (iii) the exact value of

Trace the equation of curve y^2=x^2(x+1)

Find the interval of convergence of P∞
n=0
x
n
n+4 .

Find the integral of f(x,y) = x^4 + y^2 over the region bounded by y=x , y =2x
and x = 2.

Consider the piecewise function
F(x) = - x+1, IF x <1
X-1, IF 1<x<2
5-xsquared, IF x>equalto 2
(i) Find lim x arrow 1f(x) if it exists.
(ii) Show that f (x) is continuous at x=2.
(iii) Sketch the graph of f(x)

Find the range of the function f defined by f(x,y) = 10-x^2-y^2 for all (x,y) for which x^2+y^2 <=9. Sketch two of its level curves.

f(x,y) = y^3 + ysin2x + e^(x+y) is diffrentiable at (1,-1).

it is given that f(x)=tan^-1 2x and g(x) =p tan^-1 x, where p is a contant. find the value of p for which f(1/2)=g(1/2)