Calculus Answers

Find the Taylors expansion of f(x) = Sin x at x = 0.

which of the following could be an example of a function with a domain ( - infinity, infinity) and a range (- infinity, 4)

if U=2 , V=3 , W=5 , X=5 and y=11 what is the value of each of the following expressions, assuming int variables?
1- U+V*W+X
2- U+Y%V*W+X
3- U+W / V+U*V
(thank you)

Evaluate the integral ∫ + /2 0 2cos 1 π
dx
x

Show that for any vector field F
∇.(∇×F) = 0

Trace the curve y2(x2- 9) =x4 by stating all the properties used in tracing.

1 Evaluate the limit
limh→02(−3+h)2−18h
limh→02(−3+h)2−18h
12
8
14
6
2 Evaluate the limit
limt→4t−(√3+4)4−t
limt→4t−(3+4)4−t

−38
−38

−58
−58

−18
−18

34
34

6 Find the integral with respect to x
∫cosxsinxdx

sin2x2+c

sin2x+c

cos2x2+c

sinx
7 Evaluate
∫2−1y2+y−2dy
∫−12y2+y−2dy

716

316

1716

516
8 Integrate with respect to x :
∫2−1x2(x3+4)2dx
12

12
6

512
9 Integrate with respect to x :
∫3−1x7+x2−−−−−√dx
∫−13x7+x2dx

22√
22

42√
42

4−22√
4−22

2√
2
10 Integrate with respect to x :
∫41x+1x√dx

203

20

320

-20

1 Integrate
∫(x3+3x2+2x+4)

x44+x3+x2+4x+c

x42−x3+x2+4x+c

3x44+2x3+x+c

6x4−3x2+c
2 Evaluate
∫(3x−2)6dx

(3x+2)72+c

(3x+2)721+c

(3x−2)721+c

3(3x−2)72+c
3 Evaluate
∫cos(6x+4)dx

sin(6x+4)6+c

cos(6x+4)6+c

tan(6x+4)6+c

sec(6x+4)6+c
4 Evaluate
∫3ex+5cos(x)−10sec2(x)dx

3e2+5sinx−10tanx+c

3ex+cosx−10tanx+c

3ex+5sinx−10secx+c

2ex−x−10tanx+c
5 Evalute
∫x2(3−10x3)dx

1150(3−10x3)5)+c

110(1−10x2)5)+c

115(3−20x3)5)+c

1100(3−2x3)5)+c

4 Find the
∫tan3xsec3xdx

tan2x+1

cot2x+1

sec2x+1

sec2x

5 Find
∫sec3xtanxdx

sin2x+c

cos2x+c

sec3x3+c

cos3x2+c

6 Evaluate
∫x+1x2−3x+2dx

3ln(x+2)−2ln(x+1)+c

3ln(x−2)−2ln(x−1)+c

−3ln(x−2)−2ln(x−1)+c

3ln(x−2)+2ln(x+1)+c