###
∫ e^(-4x) dx over the interval [ 0 , 1 ]

¼ - 1/(4e⁴)

###
d/dx (2x+3)/(3x+4)

-5/(3x+4)²

###
∫sinx dx over the interval [ 0 , Π/4 ]

-√2 / 2 +1

###
∫ x² cos (x³) dx

1/3 sin (x³) + C

###
if f(x) = ln ( x + 4 + e^(-3x) ) then f'(0)=

-2/5

###
d/dx x² sin(2x)

2x ( sin(2x) + x cos(2x) )

###
f'(x)=x² - 2/x then f is decreasing

( 0 , 2^(1/3)

###
If the line tangent to the graph of the function f at the point ( 1 , 7 ) passes through the point ( -2 , -2 ) then f'(1)=

3

###
f = 2x e^x then f is concave down when

( -∞, -2 )

###
y'=2x+3. Find the equation for y if it passes through the point ( 1 , 2 )

y=x²+3x-2

###
f = 4x³-5x+3. Find the equation for the tangent line to the graph of f at x=-1

y = 7x + 11

###
A particle moves along the x-axis so that at time t≥0 its position is given by x(t)=2t³-21t²+72t-53. At what time t is the particle at rest?

3 and 4

###
What is the slope of the line tangent to the curve 3y²-2x²=6-2xy at ( 3 , 2 )

4/9

###
Let f be defined by f(x)= x³+x. If g(x) is the inverse of f(x) and g(2)=1 find g'(2)

¼

###
d/dx ∫sin(t³)dt [ 0, x²]

2x sin (x⁶)

###
f(x)=( x³-2x²+3x+4)/(4x³-3x²+2x-1) find the limit as x->∞

1/4

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