LIMITS
Derivatives
The Rules
Exponential and logarithmic
Functions , min. and max.
100
lim = (2x+1)/x x→∞
lim = 2 x→∞
100
use the four -step process to find the slope of the tangent line. (show your work) f(x)= 13
m=0
100
f(x)= 2x(x^2+1)
f'(x)= 6x^2 + 1
100
f(x)= e^-2x
f'(x)= -2e^-2x
100
C(x)= 100x +200,000
average cost= 100 + 200,000/x
200
lim (2x^3 - 3x^2 +1)/(x^2 + 2x + 4) x→∞
lim = ∞ x→∞
200
use the four -step process to find the slope of the tangent line. (show your work) f(x)=2x+7
m=2
200
f(x)=(x^3 - 1)(2x+1)
f'(x)= 2(x^3 - 1) + 3x^2 (2x+1) or 8x^3 +3x^2 -2
200
f(x) = 3(e^x + e^-x)
f'(x) = 3(e^x - e^-x)
200
Find R(x) p= -0.04x + 800
R(x)= -0.04x^2 +800x
300
lim (2x^2-5x-3)/(x-3) x→3
lim = 7 x→3
300
use the four -step process to find the slope of the tangent line. (show your work) f(x)=2x^2
m=4x
300
let f(x) = (x^3+1)(3x^2 - 4x + 2) at (1,2). Find the equation of the tangent line.
y=7x-5
300
f(x)= ln( 1/x^2)
f'(x) = -2/x
300
find P'(8000) C(x)=200x +300,000 p=-0.04x+800
P'(8000) = -40
400
lim (2x+1) / (x+4) x→2
lim = 5/6 x→2
400
use the four -step process to find the slope of the tangent line. (show your work) f(x)=-x^2 +3x
m= -2x+3
400
f(x)= (x-1)^2(2x+1)^4
f'(x)= 8(2x+1)^3(x-1)^2 + 2(x-1)(2x+1)^4
400
f(x)= ln(4x^2 -5x+3)
f'(x)= (8x -5) / (4x^2 -5x+3)
400
find the relative maxima and minima g(x)= x^3 - 3x^2 +5
Relative maxima g(0) = 5 Relative minima g(2)= 1
500
lim (2x-2) / (x^3 + x^2 -2x ) x→1
lim = 2/3 x→1
500
let f(x)= 2x^2+1 a) find the derivative b) find the equation of the tangent line at (1,3)
a) 4x b)y=4x-1
500
f(x)= (3x^2 +1)^3 / (x^2 -1)^4
f'(x)= 2x(x^2 -1)^3(3x^2 +1)^2{9(x^2 - 1)-4(3x^2 +1)} / (x^2 -1)^8
500
f(x) = (e^x - 1) / (e^x +1)
f'(x) = 2e^x / (e^x+1)^2
500
find the relative maxima and minima g(x) = x^4 - 4x^2 +20
Relative minimum g(3)= -7
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