F.U.N. 🎪
Compute the following:
2+(5-7)^2\div 4*9
11
Find the slope of the line with the following points: (45,10), (57,8)
-1/6
Calculate the following limit:
lim_{x->4}x^2+3x-7
21
Find the derivative:
h(x)=4x^2+5x
h'(x)=8x+5
Solve the following:
e^x-4=6
x=ln(10)
If the parent function is
y=\sqrt(x)
, then list out the transformations for the following function:
g(x)=-3\sqrt(x-2)+7
- Reflection over the x-axis
- Vertical stretch by 3 units/horizontal compression by 3 units
- Translation 2 units right
- Translation 7 units up
Find the tangent line of
f(x)=3x^2+4x-10
at
x=-3
.
y=-14x-37
Find the limit:
lim_{x->5}(x^2-13x+40)/(x-5)
-3
Find the derivative:
(3x^2)(4x+5)
36x^2+30x
Find the derivative of the following:
3ln(2x^2+3x)
(12x+9)/(x^2+3x)
Compute
(4x+5)/6-(8-x)/3=0
7/2
List the roots for the following function:
2x^2-5x+2
(1/2,0)(2,0)
Find the limit:
lim_{x->3}(4x^2-9x-9)/((x-4)(x-3))
-15
Find the derivative:
h'(x)=40/(2x+1)^2
40/(2x+1)^2
Find the following derivative:
(ln(4-6x))/x
(((-6x)/(4-6x)-ln(4-6x)))/x^2
Compute the following:
cos((3\pi)/4), cot((11\pi)/6), sec((7\pi)/4)
-\sqrt2/2, -\sqrt3, \sqrt2/2
Find the inverse of the following function:
h(x)=(x+5)/(3x-2)
h^{-1}(x)=(-5-2x)/(1-3x)
Find the limit:
lim_{h->0}((1+h)^2-1)/h
2
Find derivative of the following logarithm:
y=ln(sin(x^2))
y'=(2xcos(x^2))/sin(x^2)
Solve the following:
3e^x-8e^-x=5
x=8/3,1
Solve the following (If you can, give ALL solutions):
sec(x)tan(x)=\sqrt3/2
x=\pi/3+n\pi
x=(2\pi)/3+n\pi
Expand the following using laws of logarithmic functions:
ln(6/\sqrt(e^3))
ln(6)-3/2
Find the limit:
lim_{x->9}(t-9)/(\sqrtt-3)
6
Find derivative of the following logarithm:
h(x)=log(sec(x))
h'(x)=(sec(x)tan(x))/(sec(x)ln(10))
Compute the derivative using logarithmic differentiation:
y=x^{\sqrtx}
y'=x^{\sqrtx-1}(2\sqrtx+\sqrtxlnx)