Question

Evaluate the integral.

pi/2 |

3
sin^{2}() cos(t)
ti + 5 sin()
cost^{4}() tj + 4
sin() cos(t)
tk dt |

0 |

Answer #1

Let h be the function defined by H(x)= integral pi/4 to x
(sin^2(t))dt. Which of the following is an equation for the line
tangent to the graph of h at the point where x= pi/4.
The function is given by H(x)= integral 1.1 to x (2+ 2ln( ln(t) ) -
( ln(t) )^2)dt for (1.1 < or = x < or = 7). On what
intervals, if any, is h increasing?
What is a left Riemann sum approximation of integral...

find g'(x)
g(x)= integral (-3/4 + t + cos(Pi/4 (t^2) + t)))
0<x<3

Evaluate the integral. (sec2(t) i + t(t2 + 1)7 j + t3 ln(t) k)
dt

use residues to evaluate the definite integral
integral (0 to 2 pi) ( d theta/ ( 5 +4 sin theta))

Compute the line integral of f(x, y, z) = x 2 + y 2 −
cos(z) over the following paths:
(a) the line segment from (0, 0, 0) to (3, 4, 5)
(b) the helical path → r (t) = cos(t) i + sin(t) j + t k from
(1, 0, 0) to (1, 0, 2π)

Given r(t)=sin(t)i+cos(t)j−ln(cos(t))k, find the unit normal
vector N(t) evaluated at t=0,N(0).

Prove the following
(4 sin(θ) cos(θ))(1 − 2 sin2 (θ)) = sin(4θ)
cos(2θ) /1 + sin(2θ) = cot(θ) − 1/ cot(θ) + 1
cos(u) /1 + sin(u) + 1 + sin(u) /cos(u) = 2 sec(u)

Evaluate 3(cos 60 + i sin 60) x 4(cos 15 + i sin 15). Write the
answer as a complex number in standard form a + bi. Round decimals
to the tenths place. (The angles are in degree form, just couldn't
use degree symbol and the x is for multiplication not a
variable.

Q1 If r(t) = (2t2
- 5)i + (t - 2)j +
(4t + 10)k, find the curvature
k(t) at t = 1.
21733
3433
4173333
3433
Q2
Find the curvature k ( t ) for r ( t ) = 8 sin t i + 8 cos t
j
Group of answer choices
1
0
−sin2t+cos2t

6.) Let ~r(t) =< 3 cos t, -2 sin t > for 0 < t < pi.
a) Sketch the curve. Make sure to pay attention to the parameter
domain, and indicate the orientation of the curve on your graph. b)
Compute vector tangent to the curve for t = pi/4, and sketch this
vector on the graph.

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