Vocabulary
Limits
Limits pt 2
Continuity
Derivatives
PQ Rules
100
Which statement describes determining a value around or approaching a point
A. Evaluate the function
B. Find the Limit
B. Find the Limit
100
lim_(x->2)f(x) =
DNE
100
When x approaches infinity, consider only the _______________ in the numerator and denominator
highest degree
100
What type of discontinuity is a hole?
Removable
100
Find the derivative of
f(x) = 5
f'(x)=0
100
What is the formula for the product rule if
k(x)=f(x)g(x)
k'(x)=f'(x)g(x)+f(x)g'(x)
200
Slope of a curve at any point.
Derivative
200
5
200
Evaluate
lim_(x->oo)f(x) =(x^2-5x+6)/(x-2)
oo
200
What type of discontinuity is an asymptote?
Essential
200
What is the derivative of
y = 3x^2 - 6x^4 + x
dy/dx = 6x - 24x^3 +1
200
f(x) = (3x - 2x^2)(5 + 4x)
f'(x)=-24x^2 + 4x + 15
300
Write the conjugate of
sqrt(x-7)+2
sqrt(x-7)-2
300
Evaluate
lim_(x->2)f(x) =(x^2-5x+6)/(x-2)
-1
300
Evaluate
lim_(x->-oo)f(x) =(x^5-5x^3+6)/(x^3-2)
oo
300
Determine the interval where the function is continuous
f(x)={(2x^3,+,9, ;, x<=-2),(x,-,5,;,x>-2):}
(-oo, oo)
300
Find the derivative of
f(x)=6sqrt(x^3)-2/x
f'(x)=9sqrt(x)+2/x^2
300
Find dy/dx if
y = 2/(x^2-5)
dy/dx=(-4x)/(x^2-5)^2
400
What is a removable discontinuity?
A. When the point is defined but the limit does not exist.
B. When the limit does not exist and the point is undefined.
C. When the
lim_(x->c)f(x)
is different from f(c).
C. When the
lim_(x->c)f(x)
is different from f(c).
400
Evaluate
lim_(x->-1)f(x) =(sqrt(x+5)-2)/(x+1)
1/4
400
Evaluate
lim_(x->-oo)f(x) =(6x^5-5x^3+4x)/(-x^5-2x^5+3)
-6
400
Determine the interval of continuity
f(x)=(x^2-2x-8)/(x^2-7x+12)
(-oo, 3)u (3, 4)u (4, oo)
400
What is the slope of the tangent line at x=4
f(x)=5sqrt(x)
5/4
400
Find the derivative of
y = (5x - 2)/(x^2 + 1)
dy/dx=(-5x^2 + 4x + 5)/(x^2 + 1)^2
500
What is a Jump discontinuity?
A. When the point is defined but the limit does not exist.
B. When the limit does not exist and the point is undefined.
C. When the
lim_(x->c)f(x)
is different from f(c).
A. When the point is defined but the limit does not exist.
500
Evaluate
lim_(x->0)f(x) (x)/(1/2-1/(x+2))
4
500
Evaluate
lim_(x->-oo)f(x) =(x^5-5x^3+7x)/(-x^7-2x^5+3)
0
500
Determine the interval where the function is continuous
f(x)={(-3x^2+16 ;x<-4),(x^3; x>=-4):}
(-oo, -4) u [-4, oo)
500
What is the equation of the tangent line at x=1
f(x)=2/sqrt(x^3)
y=-3x+5
500
f(x) = x^2sin( x)
Find f'(x)
2xsin( x)+x^2cos(x)
600
Limits as x approaches infinity focus on the ________________ and _________________
Horizontal Asymptotes and Slant Asymptotes
600
Evaluate the limit
lim_(x->1)(-x)/(x-1)^2=
-oo
600
Evaluate
lim_(x->oo)f(x) =(x^5-5x^3+7x^8)/(-x^6-2x^5+3)
-oo
600
Determine the interval where the function is continuous
f(x)={(5x^2-10 ;x=-2),(x^3; x!=-2):}
(-oo, -2) u (-2, oo)
600
What is the equation of the Normal line at x=0
f(x)=2sqrt(x^3)+2x-5
y=-1/2x-5
600
Find the derivative of
f(x) = 4cos x
-4 sin x