Calculus Answers

Evaluate the following integral using Stokes theorem

Integralof over C (x+z)dx+(x-y)dy+xdz)

Where C is an ellipse

(x^2/16)+(y^2/25)=1 z=4

Find the points on the graph of the function f(x)=x+1/x-1 where the slope of the tangent line is equal to -1/3 Determine the equations of the tangent and normal line.

Find all points on the graph of the equation x2-y2=2x+4y where the tangent line is horizontal. Does the graph have any vertical asymptote? Sketch the graph

Find the point(s) on the graph of the function where the slope of the tangent line is equal to . Determine the equations of the tangent and the normal lines.
(b) Discuss the curve under all relevant headings.

Find the area of the region inside both the rose curve r=sin⁡〖(2θ)〗 and the circle r=cos⁡θ. Choose the most appropriate graph and intervals to the best of your interest to solve this question

Determine the work done by a force
F=(xy+3z)i(cap) + (2y^2-x^2)j(cap) + (z-2y) k(cap) in taking a particle from x=0 to x=1 along a curve defined by equation

x^2=2y ; 2x^3=3z

Two functions f and g are defined on the set of real numbers, R, by
f : x = x/2-x
g : x = px + q, where p and q are constants.
(i) Find g^−1
(ii) Given that g^−1(4) = 2 and g ◦ f(4) = −8, find the values of p and q

Two functions f and g are defined on the set R of real numbers by
f(x) = ax^2 + bx − 2 and g(x) = 3x + 2. If f(1) = 7 and f(2) = 10. Find:
(a) the values of a and b;
(b) the value(s) of x if f(x) = g(x) − 1.