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Popular Calculus Problems
sum from n=1 to infinity of n^4(1+n^5)^2
∑
n
=
1
∞
n
4
(
1
+
n
5
)
2
limit as x approaches 0 of (sin(40))/x
lim
x
→
0
(
sin
(
4
0
)
x
)
derivative of f(x)= 3/(x+3)
derivative
f
(
x
)
=
3
x
+
3
integral of cos(5x)cos(7x)
∫
cos
(
5
x
)
cos
(
7
x
)
dx
integral from 0 to 3 of-x^2+9
∫
0
3
−
x
2
+
9
dx
y^'=((y^2-1))/(2x),y(1)=-2
y
′
=
(
y
2
−
1
)
2
x
,
y
(
1
)
=
−
2
(dy}{dt}=-\frac{3y)/t-2-t^{-4},y(1)=4
dy
dt
=
−
3
y
t
−
2
−
t
−
4
,
y
(
1
)
=
4
limit as x approaches 2 of sqrt(x)
lim
x
→
2
(
√
x
)
area x,x^3,4x,0
area
x
,
x
3
,
4
x
,
0
inverse oflaplace 1/(6s+1)
inverselaplace
1
6
s
+
1
area f(x)= 1/x ,g(x)=-1/3 x+3,[0,12]
area
f
(
x
)
=
1
x
,
g
(
x
)
=
−
1
3
x
+
3
,
[
0
,
1
2
]
integral from 0 to 1 of (4x)/(e^{x^2)}
∫
0
1
4
x
e
x
2
dx
(\partial)/(\partial x)((x^2+y^2+z^2)^{0.5})
∂
∂
x
(
(
x
2
+
y
2
+
z
2
)
0
.
5
)
integral of (4-x)/(x^4-x^2)
∫
4
−
x
x
4
−
x
2
dx
limit as x approaches 2 of 2x+c
lim
x
→
2
(
2
x
+
c
)
f(x)=(1-ln(x))/(2x^2)
f
(
x
)
=
1
−
ln
(
x
)
2
x
2
(dy)/(dx)=|x-2|
dy
dx
=
|
x
−
2
|
tangent of f(x)=(x^2-4)^2
tangent
f
(
x
)
=
(
x
2
−
4
)
2
d/(dt)(acos(t))
d
dt
(
a
cos
(
t
)
)
inverse oflaplace 3/((s+1)^3)
inverselaplace
3
(
s
+
1
)
3
derivative of f(x)=(sqrt(x))/(1+x)
derivative
f
(
x
)
=
√
x
1
+
x
f(x)=4x^3
f
(
x
)
=
4
x
3
(dx)/(dt)=x+e^t
dx
dt
=
x
+
e
t
derivative of 3sqrt(x)+2/(5x^3-sqrt(2))
d
dx
(
3
√
x
+
2
5
x
3
−
√
2
)
integral of sin^4(t)
∫
sin
4
(
t
)
dt
x((dy)/(dx))-3y=x^3,y(1)=1
x
(
dy
dx
)
−
3
y
=
x
3
,
y
(
1
)
=
1
(dy)/(dx)= y/x-(x^2)/(y^2)
dy
dx
=
y
x
−
x
2
y
2
limit as x approaches 0+of (ln(x))/(x^2)
lim
x
→
0
+
(
ln
(
x
)
x
2
)
(dy)/(dt)=5y+y^5
dy
dt
=
5
y
+
y
5
derivative of x-1/(3x^3)
derivative
x
−
1
3
x
3
tangent of y=x^2-2x-3
tangent
y
=
x
2
−
2
x
−
3
(dy}{dx}=\frac{xy)/8
dy
dx
=
xy
8
derivative of x^2+2x+4
derivative
x
2
+
2
x
+
4
inverse oflaplace 1/(s(s+2)(s+6))
inverselaplace
1
s
(
s
+
2
)
(
s
+
6
)
integral from-1 to 1 of 1/(x^2-1)
∫
−
1
1
1
x
2
−
1
dx
sum from n=0 to infinity of 1800(1/3)^n
∑
n
=
0
∞
1
8
0
0
(
1
3
)
n
tangent of f(x)=4xe^x,(0,0)
tangent
f
(
x
)
=
4
xe
x
,
(
0
,
0
)
integral of x(4+x)^{10}
∫
x
(
4
+
x
)
1
0
dx
derivative of (2(1-ln(x)))/(x^2)
derivative
2
(
1
−
ln
(
x
)
)
x
2
limit as x approaches-2 of 3x^2+5x-1
lim
x
→
−
2
(
3
x
2
+
5
x
−
1
)
integral of t/((t^2+1)^{5/2)}
∫
t
(
t
2
+
1
)
5
2
dt
integral of 1/(16x^2+7)
∫
1
1
6
x
2
+
7
dx
derivative of (13)/x
derivative
1
3
x
d/(dt)(e^{7tsin(2t)})
d
dt
(
e
7
t
sin
(
2
t
)
)
limit as x approaches 0 of sin(1/x)
lim
x
→
0
(
sin
(
1
x
)
)
integral of xcsc(x^2)cot(x^2)
∫
x
csc
(
x
2
)
cot
(
x
2
)
dx
integral of 1/((x^2+25))
∫
1
(
x
2
+
2
5
)
dx
derivative of y= 5/7 x+4/3
derivative
y
=
5
7
x
+
4
3
y^{''}+2y=3,y(0)=-1,y^'(0)=2
y
′
′
+
2
y
=
3
,
y
(
0
)
=
−
1
,
y
′
(
0
)
=
2
derivative of log_{5}(2x^3+x^2)
d
dx
(
log
5
(
2
x
3
+
x
2
)
)
integral of (13)/(r^2+1)
∫
1
3
r
2
+
1
dr
e^xy(dy)/(dx)=e^{-y}+e^{-8x-y}
e
x
y
dy
dx
=
e
−
y
+
e
−
8
x
−
y
(\partial)/(\partial x)((5y^4)cos(5x))
∂
∂
x
(
(
5
y
4
)
cos
(
5
x
)
)
tangent of f(x)=sqrt(x+5),(11,4)
tangent
f
(
x
)
=
√
x
+
5
,
(
1
1
,
4
)
derivative of h(t)=(t+2)^{2/3}(2t^2-3)^3
derivative
h
(
t
)
=
(
t
+
2
)
2
3
(
2
t
2
−
3
)
3
derivative of (e^{3x}+e^{-3x}/x)
d
dx
(
e
3
x
+
e
−
3
x
x
)
(dy)/(dt)=(-csc(t)cot(t))e^{-csc(t)}
dy
dt
=
(
−
csc
(
t
)
cot
(
t
)
)
e
−
csc
(
t
)
limit as x approaches infinity of-3x^3
lim
x
→
∞
(
−
3
x
3
)
limit as x approaches 0-of 1-x^2
lim
x
→
0
−
(
1
−
x
2
)
limit as x approaches 0 of (1-4x)^{7/x}
lim
x
→
0
(
(
1
−
4
x
)
7
x
)
sum from n=1 to infinity of (35)/(-6^n)
∑
n
=
1
∞
3
5
−
6
n
integral of sin(θ/2)
∫
sin
(
θ
2
)
d
θ
y^{''}-9y=(x^2-5)sin(3x)
y
′
′
−
9
y
=
(
x
2
−
5
)
sin
(
3
x
)
area y=7x,y=x^2-8,y=0
area
y
=
7
x
,
y
=
x
2
−
8
,
y
=
0
(dy)/(dx)=2x+xy
dy
dx
=
2
x
+
xy
derivative of (x^{-2}+x^3(4x)^{-2})
d
dx
(
(
x
−
2
+
x
)
3
(
4
x
)
−
2
)
integral of 3tan^5(x)
∫
3
tan
5
(
x
)
dx
integral of (1-5y)
∫
(
1
−
5
y
)
dy
derivative of arcsin(ln(x))
d
dx
(
arcsin
(
ln
(
x
)
)
)
inverse oflaplace 1/(s^2-3s+2)
inverselaplace
1
s
2
−
3
s
+
2
derivative of arctan(sqrt(5x^2-1))
derivative
arctan
(
√
5
x
2
−
1
)
(d^2y)/(dx^2)+2(dy)/(dx)=1+9x^2
d
2
y
dx
2
+
2
dy
dx
=
1
+
9
x
2
integral of 3sec^4(x)
∫
3
sec
4
(
x
)
dx
limit as x approaches (3pi)/4 of-2sec(x)
lim
x
→
3
π
4
(
−
2
sec
(
x
)
)
(dx)/(dt)=6*0.3-5*x/(100+t),x(0)=0
dx
dt
=
6
·
0
.
3
−
5
·
x
1
0
0
+
t
,
x
(
0
)
=
0
derivative of f(x)=2*7^{2x^2+3}
derivative
f
(
x
)
=
2
·
7
2
x
2
+
3
integral of ((x^3))/(sqrt(x^2+25))
∫
(
x
3
)
√
x
2
+
2
5
dx
(\partial)/(\partial t)(scos(t))
∂
∂
t
(
s
cos
(
t
)
)
derivative of sqrt(x+y)
d
dx
(
√
x
+
y
)
taylor x-x^3,-2
taylor
x
−
x
3
,
−
2
(\partial)/(\partial y)(3xz^2e^{y^2})
∂
∂
y
(
3
xz
2
e
y
2
)
derivative of f(x)= 1/x+1/(x^2)+1/(x^3)
derivative
f
(
x
)
=
1
x
+
1
x
2
+
1
x
3
(tdy)/(dt)+(t+1)y=t
tdy
dt
+
(
t
+
1
)
y
=
t
derivative of y=be^{e^3+x^3}
derivative
y
=
be
e
3
+
x
3
derivative of 2log_{10}(x-3sqrt(x))
d
dx
(
2
log
1
0
(
x
)
−
3
√
x
)
integral of (2x^2)/(sqrt(4x-x^2))
∫
2
x
2
√
4
x
−
x
2
dx
derivative of (3x+4)/(3x-4)
derivative
3
x
+
4
3
x
−
4
integral of sec^5(x)-sec^3(x)
∫
sec
5
(
x
)
−
sec
3
(
x
)
dx
x(y+1)dx+y(x-1)dy=0
x
(
y
+
1
)
dx
+
y
(
x
−
1
)
dy
=
0
limit as x approaches 0 of x/(x^2-1)
lim
x
→
0
(
x
x
2
−
1
)
derivative of 1/(x(ln(x)))
d
dx
(
1
x
(
ln
(
x
)
)
)
81y^{''}+108y^'+66y=0,y^'(0)=2,y(0)=6
8
1
y
′
′
+
1
0
8
y
′
+
6
6
y
=
0
,
y
′
(
0
)
=
2
,
y
(
0
)
=
6
tangent of sqrt(1-x)
tangent
√
1
−
x
derivative of (9x/(64+x^2+y^2))
d
dx
(
9
x
6
4
+
x
2
+
y
2
)
derivative of-ln|cos(x|)
d
dx
(
−
ln
|
cos
(
x
)
|
)
derivative of f(x)=(-3x^2-3)^4
derivative
f
(
x
)
=
(
−
3
x
2
−
3
)
4
limit as t approaches 0 of cos(3t)
lim
t
→
0
(
cos
(
3
t
)
)
(\partial)/(\partial z)(((x+y))/((y+z)))
∂
∂
z
(
(
x
+
y
)
(
y
+
z
)
)
integral of (e^θ)/(a+be^θ)
∫
e
θ
a
+
be
θ
d
θ
integral of 4-3(1+x^2)^{-1}
∫
4
−
3
(
1
+
x
2
)
−
1
dx
1
..
527
528
529
530
531
..
2459