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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 > .
(a) Find the value of Z C (x + y) ds, where C is parameterized by x = t, y = t and 0 ≤ t ≤ 1
) Calculate integral R C F · dr · dr, where F(x, y, z) =< 2x ln y, x 2 y + z 2 , 2yz >, and C is a curve with a parameterization r(t) =< t2 , t, t >, 1 ≤ t ≤ e
