Calculus Answers

Find the point on the terminal side of θ = three pi divided by four that has a y coordinate of 1.

Give an example of a rational function that has a horizontal asymptote at y = 1 and a vertical asymptote at x=4 .

Compute the Jacobian matrices using the chain rule for z = u^2 + v^2 where
u = 2x + 7, v = 3x + y + 7

find dw/dt at t=π/2, where

w= x^2+y^2+2x+3y, x=cos t, y= sin t

Can L’Hopital’s rule be applied to evaluate the limit

lim 1-sin x / cos x
x->π/2

Find the domain of the following. Find the domain of the following functions f and evaluate f (3,2) . functions f and evaluate f (3,2) .

1) f(x,y) = √(x+y+1) / x-1

2) (x,y) = x ln(y^2-x)

Evaluate the limits

lim l n tan 2x / l n tan x
x-> 0^+

Evaluate the limits:


lim = (sin 1/x) / (e^(1/x) -1)
x-> -∞

Find the direction in which the function f = X^2-Y^2-2XY decreases most rapidly at
the point (1,1)

Find the inverse of the function.

f(x) = x3 + 8


he lp me please