Calculus Answers

Find all numbers at which f is not continous for the given functions. Answers must be written in interval notation.

a. g(x) = x+5/x²+6x+8

b. f(x) = (3/x²) + (2/x+4) - (x/2x-3)

c. f(x) = x/(x³-x²)

d. f(x) = [(sqrtx)+10]/x

e. f(x) = 2x/x(sqrt x+4)

f. f(x) = ln srqt(x+6/4x²-9)

g. f(x) = ln srqt(x-8/x+3)

h. f(x) = [(sqrtx)+5]/4-(sqrt x)

i. f(x) = x-1/(sqrt x²-3x+2)

j. f(t) = sin^-1 (2t-3)

Find lim h→0 f(h+3)-f(3)/h

a. f(x) = x²-3

b. f(x) = x/x-2

c. f(x) = sqrt x+1

Find the limit of each given transcendental function as x→c

a. lim x→-1 (2ln x+3/2x+5)

b. lim x→0 (e^3x - 1/ e^x -1)

c. lim x→0 (2^2x - 2^x+1 +1 / 2^x -1)

d. lim x→0 (3tan²x/2x²)

e. lim x→0 (1-cos2x/sin2x)

f. lim θ→0 (5θ/tan2θ)

g. lim x→0 (2x²-6x/sin2x)

h. lim t→0 [4t²/(1-cos² (t/2))]

Find lim as h→0 f(x+h)-f(x)/h

a. f(x) = 1-x/x+2

b. f(x) = sqrt x²-3

Find the equations of the vertical and horizontal asymptotes of the graphs of the given rational functions.

a. f(x) = 4x²-3x+2/x²-3x+2

b. f(x) = x²-x-20/x²-7x+10

c. f(x) = 4x²-9/2x²-5x+3

d. f(x) = [(4/x-6)+(2/3)]/x

e. f(x) = (4/x²-1)+(2/x+1)

) If F(x, y, z) = e xˆi + yzˆj − yz2ˆk, find the divergence of F at (0, 2, −1)

Use Green’s theorem to calculate the area enclosed by the ellipse x 2 a 2 + y 2 b 2 = 1. Where F(x, y) =< P, Q >=< y 2 , x 2 >.

Use Greens theorem to calculate the line integral H C x 2ydx + (y − 3)dy,, where C is a rectangle with vertices (1, 1), (4, 1), (4, 5) and (1, 5), oriented counterclockwise.

) Find the value of integral Z C F · dr, where C is a semicircle parameterized by vecsr(t) = cost,sin t, 0 ≤ t ≤ π, and F =< −y, x > .