Calculus Answers

How to solve binomial expansion of (2+x)^(-1/2)

. Find the value of x and the value of y in the following equation. 𝟏 𝒙+𝒚𝒊 - 𝟏 𝟏+𝒊 = 2 – 3i

A. Assuming a two-terminal circuit element with impedance Z = 2.3 + 5i is driven by a sinusoidal current I = 𝒊(𝟎.𝟒𝟐−𝟑.𝟔𝒊) 𝟑.𝟓+𝟐.𝟓𝒊 . Find the voltage of the circuit (according to Ohm’s law V = IZ). 

If f is continuous and "\\intop f (x) dx=6 (upper limit=2, lower limit=0)" ,evaluate

"\\intop f(2sin\\theta) cos\\theta d\\theta (upper limit=\\pi\/2 ,lower limit=0)"

Assume that a particle is at the origin when the time t is at the origin

Determine the position vector of the velocity of the particle at time t given the velocity as

V(t)=e^-ti+5e^-2tj

find the maximum and minimum points of the function x³-x²

find the limit at infinity of (2+x)30 x (4+x)5 / (2-x)35

i) A particle moves along a line with velocity function v(t)= (t² - t), where v is measured in meters per second. Find (a) the displacement and (b) the distance traveled by

the particle during the time interval [ 0, 5]

ii) Use the properties of integrals to verify the inequality.

Integral of "\\intop (sinx\/x) dx" Upper limit ("\\pi" /2) and Lower limit ("\\pi" /4) <= ( √2 / 2) .

iii).Evaluate the intregal, if it exists.

1. "\\intop (1+ tan t)" ³ sec²t dt ( Upper limit ("\\pi" /4) and Lower limit (0)
2. "\\intop\\begin{vmatrix}\n \u221ax - 1 \\\\\n\n\\end{vmatrix}" dx (Upper limit (4) and Lower limit (0)
3. "\\intop"tan x ln(cos x) dx

Evaluate the integral "\\displaystyle{\\int_{1}^{e}(\\ln{x})^{2}dx}\u222b" using the integration by parts twice

1. e-2
2. e+2
3. e
4. 1/e

Evaluate the integral "\\displaystyle{\\int_{0}^{\\pi\/2}\\sin{(x)}\\ln{\\sec{(x)}}dx}"

1. 1
2. 0
3. 1/2
4. 8