Integrals
int_0^3x/sqrt(x^2+16)dx
1
if y=ln(3x+5) , then (d^2y)/(dx^2)=
-9/((3x+5)^2
does the series converge or diverge?
sum_(n=1)^oo(4n+2)/((n+1)^2)
diverge
if int_2^8f(x)dx=-10 and int_2^4f(x)dx=6 , then int_8^4f(x)dx=
16
what is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y=12-x^2
32
int_0^2xe^xdx
e^2+1
Find an equation of the line tangent to the curve at the point (1, 7)
y=(3x+4)/(4x-3)
y-7=-25(x-1)
what is the value of
sum_(n=1)^oo3^(n+1)/4^n
9
the Maclaurin series for a function f is given by sum_(n=1)^oox^n/(2n)
what is the value of f^(4)(0) ?
3
what is the approximate value of cos(1/2) obtained by using a fourth degree Taylor polynomial for cosx about x=0
0.877
int_-1^1dx/(x^2+5x+6)
ln(3/2)
what are the values of x for which the graph of y=6x^2+x/2+3+6/x is concave down?
-1 < x < 0
what are all values of p for which int_1^oo1/x^(pip)dx converges?
p>1/pi
if g(x)=e^(2x) , then what is lim_(h->0)(g(1+h)-g(1-h))/h
4e^2
what is the area enclosed by the polar curve r=6costheta+8 from theta=0 to theta=pi
78.540
the efficiency of an automobile engine is given by the continuous function r(c) where r is measured in liters/kilometer and c is measured in kilometers
what are the units of int_0^5r(c)dc
liters
the position of a particle in the xy-plane is given by x=4t^2 and y=sqrtt
at t=4 , what is the acceleration vector?
<8,-1/32>
find the interval of convergence
sum_(n=2)^oo(-1)^n/(lnn)x^n
-1<x<=1
if x=2t^2 and y=t^3 , then (d^2y)/(dx^2) at t=3 is
1/16
if the following is true, what is the value of a?
int_0^(1000)8^xdx-int_a^(1000)8^xdx=10.40
1.500
if (dy)/(dx)=ycosx and y=3 when x=0 , then y=
3e^(sinx)
lim_(h->0)(2(x+h)^5-5(x+h)^3-2x^5+5x^3)/h is
10x^4-15x^2
the power series for 1/(x+1) is sum_(n=0)^oo(-1)^nx^n
find the first four terms of the power series for
x^2/(1+x^4)
x^2-x^6+x^10-x^14
express the following as an integral
lim_(n->oo)1/n[1/(1+1/n)+1/(1+2/n)+...+1/(1+n/n)]
int_1^(2)1/xdx
an antiderivative of f is (tan^2x)/(x^2+1) where f(1)=1/2
what is f(0) ?
0.155