Calculus Final Exam
If x²+xy=10, then when x=2, (dy)/(dx)=
(-7/2)
If f(x)=sin(e^-x), then f'(x)=
(-e^-x)cos(e^-x)
The function f is given by f(x)=x⁴+x²-2 on which of the following intervals is f increasing
(0, positive infinity)
y=3x²-x³ relative maximum at ?
(2,4)
if f''(x)=x(x+1)(x-2)², then the graph of f has inflection points when x=
-1,0,2
IF f(x) = ln(x+4+e⁻³), then f'(0) is
-2/5
What is the x coordinates of the points of inflection on the graph of y=(1/3)x³+5x²+24
-5
If y=(2x+3)/(3x+2), then (dy)/(dx)=
-5/(3x+2)²
If f(x)=(x²-9)/(x+3) is cont. @ x=-3 f(-3)= ?
-6
if e^xy=2, then at thee point (1,ln2), (dy)/(dx)=
-ln(2)
If y=(1-x)/(x-1), then (dy)/(dx)=
0
lim (10⁸x⁵+10⁶x⁴+10⁴x²)/(10⁹x⁶+10⁷x⁵ +10⁵x³)
0
For what value of x does 4x⁶-8x³+18 have a relative minimum
1 only
the position of a particle on the x-axis at the time t, t>0, is ln(t). The average velocity of the particle for 1≤t≤e is
1/(e-1)
lim (x³-2x²+3x-4)/(4x³-3x²+2x-1)
1/4
The which of the following statements are true one I. f(X) is cont. II. f'(x) is the derivative of f(x) III. The graph of f(X) concave upwards
I only
If f(x) = 3+ |x-2|, then f'(2)
Nonexistent
If f(x)={lnx for 0<x≤2;x²ln2 for 2<x≤4, then lim f(x) is
Nonexistent
lim (x²+3x)/(√(x²+6x+9)) is
Nonexistent
A particle moves along the x-axis in such a way that is position at time t is given by x(t)=(1-t)/(1+t). What is the acceleration of the particle at time t=0?
4
The maximum value of f(x)= 2x³-9x²+12x-1 on [-1,2] is
4
What is the slope of the line tangent tot he curve 3y²-2x²=6-2xy at the point (3,2)
4/9
The equation of the tangent line to the curve x²+y²=169 at the point (5,-12) is
5x-12y=169
If y= (x³+1)², then (dy)/(dx)=
6x²(x³+1)
Two cars start at the same place and at the same time. One car travels west at a constant speed of 50 miles per hour and a second car travels south at a constant speed of 60 miles per hour. Approximately how fast is the distance between them changing one-half hour later
78 miles per hour
If f(x) = tan(2x), then f'(π/6)
8
The volume of an expanding sphere is increasing at a rate of 12 cubic feet per second. When the volume of the sphere is 36π cubic feet, how fast, in square feet per second, is the surface area increasing?
8
The graph of which function has y=-1 as an asymptote
y=(x/(1-x))
Let f be the function defined by f(x) = 4x³-5x+3. Which of the following is an equation of the line tangent to the graph of f at the point where x=-1
y=7x+7
An equation of the line tangent to the graph of y=x+cosx at the point (0,1) is
y=x+1
if f(x)= √(4sinx+2), then f'(0)=
√2
If f(x)=e^(sinx), how many zeros does f'(x) have on the closed interval [0,2π]
2
If the graph of f(x)=2x²+(k/x) has a point of inflection at x=-1, then the value of k is
2
What is the instantaneous rate of change at x=2 of the function f given by f(x)= (x²-2)/(x-1)
2
The maximum acceleration attained on the interval 0≤t≤3 by the particle whose velocity is given by v(t)=t³-3t²+12t+4
21
lim (tan2(x+h)-tan(2x))/(h) is
2sec²(2x)
If y=x²sin2x, then (dy)/(dx)
2x(sin2x+xcos2x)
lim (b-x)/(√(x)-√(b)) is
2√b
A particle moves along the x-axis so that its position at time t is given by x(t)=t³-6t+5. For what value of t is the velocity of the particle zero
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) is
3
if f(x)=3xlnx,then f'(x)=
3+ln(x³)
d/dx(e^3lnx)=
3x²
Which of the following are the equations of all horizontal and vertical asymptotes for the curve y=(x)/(x(x²-4))
HA: y=0 VA: x=-2 and x=2
The minimum value of f(x)=e^x-2x is
ln(2)
If y= x(lnx)², then (dy)/(dx)=
lnx(2+lnx)
At how many points on the curve y=4x⁵-3x⁴+15x²+6 will the line tangent to the curve pass through the origin
one
A particle moves along the x axis so that its position any time t>0 is given by x(t)=t⁴-10t³+29t²-36t+2
t=4
At the point of intersection of f(x) = cosx and g(x)=1-x², the tangent lines are
the same lines
For what values of x is the graph of y=2/(4-x) concave downward?
x>4
