Show:
Sequences and Binomials
Functions and Logarithms
Limits
Tangent Lines and f'(x)'s
Derivatives
100
If r=4 and a6=192, find a1.
a1=-576
100
Evaluate log(base7)(7)^3
3
100
Find the limit if it exists of: lim((n^3)-2)/(n^2)
limit does not exist because the numerator is larger than the denominator (power-wise)
100
Using the definition of derivatives find the derivative of: y=(1/x)
-(1)/(a^2)
100
Find the derivative of 2(x^3)-9x+5(x^2)+3
6(x^2)-9+10x
200
Expand (2x-3y)^5
2(x^5)-30(x^4)y-60(x^3)(y^2)-60(x^2)(y^3)-30x(y^4)-3(y^5)
200
Write (1/4)^-4=256 in logarithmic form
log(base 1/4)(256)=-4
200
Find the horizontal and vertical asymptotes for the function: f(x)=(x-1)/((x^2)-3x+2)
horizontal: y=0 vertical: x=2
200
Using the definition of derivatives find the derivative of: ((x^2)+1)/(x-4)
(a^2)-8a-1
200
Find the derivative of: tan(sin(e^x))
sec^2(sin(e^x))(cos(e^x)e^x)
300
Find the 6th term of the sequence (2p-3r)^11
462(p^6)(r^5)
300
Find f*g and g*f if: f(x)=(x+1)^2 and g(x)=cos(x)
f*g=(cos(x)+1)^2 g*f=cos(x+1)^2
300
Prove lim(as x approaches 1) of 3x-4=-1
0
300
Using the definition of derivatives find the derivative of 2x-1
2
300
Find the derivative of: (2(x^2)+4x+1)(4(x^3)+7x-4)
(2(x^2)+4x+1)(12(x^2)+7)+(4(x^3)+7x-4)(4x+4)
400
Find the sum of the first 50 terms in the series: -25, -21, -17...
3,650
400
Find (f(a+h)-f(a))/h of (x^2)-2x+5
2a-2
400
Given f(x)={(x+2, when x<=-1), ((x^2), when -1=1)}
Yes
400
Find the instantaneous velocity if the position function is f(x)=2(t^3)-3t+5 at t=a
6(a^2)-3
400
Find the derivative of (x+2)/((x^2)+3x-4)
(((x^2)+3x-4)-(x+2)(2x+3))/(((x^2)+3x-4)^2)
500
Use the ratio test to determine whether the series is convergent or divergent. (4/3)+(4/9)+(4/27)...
Convergent
500
Change the base to find the value of log(base11)47
x=(ln47)/(ln11)
500
Evaluate the limit using the Squeeze Theorem of: lim(as x approaches 0) of (x^2)cos(3/x)
By the Squeeze Theorem, lim(as x approaches 0) of (x^2)cos(3/x)=0
500
Find the equation of the tangent line to the parabola y=(x^2)+6x at x=3
y-27=12(x-3)
500
Find the derivative of: (e^((x^2)+3))(4(x^3)+6x)^2
(e^(x^2)+3)2(4(x^3)+6x)(12(x^2)+6)+((4(x^3)+6x)^2)(e^(x^2)+3)(2x)