Limit, Continuity, Curve Sketching
Take the limit x->inf
3x^2 + 9x - 3
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5x^2-9
3/5
If f(s) = (s − 1) /(s + 1) , find f' (1).
1/2
Derive the function: y=e^(3x)
3e^(3x)
Find Vertical & Horizontal Asympt.
x^2-5x+6
------------------
x^3-8x^2+15x
y=0
x=0, x=5
Find eq. tangent line of y=x^2lnx at (1,0)
y=x-1
How long will it take $5,000 to grow to $10,000 if the investment earns an interest rate of 8% per year compounded quarterly?
Hint: use A = P(1+r/m)^(mt)
t= ln2
----------
4ln(1.02)
Integrate
(x^3 +x^2 − x + 1)/x^2
x^2/2 + x -ln|x|-1/x +C
y^2-xy-8x+6=0 Find dy/dx at (1,2)
dy/dx = 10/3
For the demand x + 2p = 60, where p represents the price in dollars and x the number of units, determine the elasticity of demand when the price p is equal to $15.
E=1
Integrate
e^3x
-----------
1 + e^3x
1/3 ln (1 + e^3x ) + C
Let f(x) =
x if x ≤ 2
x^ 2 − 3x + 4 if x > 2
Which of the following is true?
a) f(x) is continuous at x = 2 but not differentiable at x = 2.
b) f(x) is differentiable at x = 2 but not continuous at x = 2.
c) f(x) is neither continuous nor differentiable at x = 2.
d) f(x) is both continuous and differentiable at x = 2
Continuous and differentiable at x=2
Sales of the Penn State Learning Calculus tutorial software packages in the first t years of its operation are approximated by f(t) = 2t/( t^ 2 + 1 ). What are the average yearly sales over the time interval 1 ≤ t ≤ 3?
(1/2)*ln|5|
Find the area of the region in the first quadrant that is enclosed by the graphs of y = √ x and y = x.
1/6
If y = (x + 3)^x , find y'(1). (Hint: Use logarithmic differentiation.)
4ln4 + 1
Integrate:
xe^(x/3)
Hint: Integration by Parts
3xe^(x/3) - 9e^(x/3)+C