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CALCULUS AND ANALYSIS
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Differential equations
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Here's what students ask on Calculus and Analysis
Parametric equations, polar coordinates, and vector-v
asked 2021-03-18
to what property does (-6 + 3 ) + 1 = -6 + (3 + 1) belong to
Multivariable functions
asked 2021-03-18
Write formulas for the indicated partial derivatives for the multivariable function.
\(\displaystyle{f{{\left({x},{y}\right)}}}={7}{x}^{{2}}+{9}{x}{y}+{4}{y}^{{3}}\)
a)
\(\displaystyle\frac{{\partial{f}}}{{\partial{x}}}\)
b)(delf)/(dely)ZSK
c)
\(\displaystyle\frac{{\partial{f}}}{{\partial{x}}}{\mid}_{{{y}={9}}}\)
Laplace transform
asked 2021-03-18
Determine
\(L^{-1}\left[\frac{(s-4)e^{-3s}}{s^2-4s+5}\right]\)
Laplace transform
asked 2021-03-18
Obtain the Laplace Transform of
\(L\left\{e^{-2x}+4e^{-3x}\right\}\)
Rational exponents and radicals
asked 2021-03-18
The simplified form of the expression
\(\displaystyle{\sqrt[{{3}}]{{a}}}{\sqrt[{{6}}]{{a}}}\ \text{in radicalnotation is}\ \sqrt{a}.\)
Transformation properties
asked 2021-03-18
For large value of n, and moderate values of the probabiliy of success p (roughly,
\(0.05\ \Leftarrow\ p\ \Leftarrow\ 0.95\)
), the binomial distribution can be approximated as a normal distribution with expectation mu = np and standard deviation
\(\sigma = \sqrt{np(1\ -\ p)}\)
. Explain this approximation making use the Central Limit Theorem.
Parametric equations, polar coordinates, and vector-valued functions
asked 2021-03-18
Write a short paragraph explaining this statement. Use the following example and your answers Does the particle travel clockwise or anticlockwise around the circle? Find parametric equations if the particles moves in the opposite direction around the circle. The position of a particle is given by the parametric equations
\(x = sin t, y = cos t\)
where 1 represents time. We know that the shape of the path of the particle is a circle.
Differential equations
asked 2021-03-12
How to integrate
\(\displaystyle{{\cos}^{{2}}{\left({2}{x}\right)}}\)
?
Green's, Stokes', and the divergence theorem
asked 2021-03-12
Use Green's Theorem to evaluate the line integral
\(\displaystyle\int_{{C}}{\left({y}+{e}^{{x}}\right)}{\left.{d}{x}\right.}+{\left({6}{x}+{\cos{{y}}}\right)}{\left.{d}{y}\right.}\)
where C is triangle with vertices (0,0),(0,2)and(2,2) oriented counterclockwise.
a)6
b)10
c)14
d)4
e)8
f)12
Transformation properties
asked 2021-03-12
Complete the tasks to determine:
a)To graf: The function
\(g{{\left({x}\right)}}={2}^{{{x}-{4}}}.\)
b)The domain of the function
\(g{{\left({x}\right)}}={2}^{{{x}-{4}}}\)
in the interval notation.
c)The range of the function
\(g{{\left({x}\right)}}={2}^{{{x}-{4}}}\)
in the interval notation.
d)The equation of the asymptote of the function
\(g{{\left({x}\right)}}={2}^{{{x}-{4}}}.\)
Integrals
asked 2021-03-11
A variable force of
\(\displaystyle{9}{x}−{29}{x}−{2}\)
pounds moves an object along a straight line when it is xx feet from the origin. Calculate the work done in moving the object from
\(\displaystyle{x}={1}{f}{t},\to,{P}{S}{K}{x}={19}{f}{t}.\)
(Round your answer to two decimal places.)
Laplace transform
asked 2021-03-11
\(\displaystyle{y}'={6}\frac{{x}^{{2}}}{{{2}{y}+{\cos{{y}}}}}{)}\)
Differential equations
asked 2021-03-11
\(\displaystyle{\left({b}\right)}{y}{''}+{y}′+{3}⋅{a}{5}{y}={0}\)
Green's, Stokes', and the divergence theorem
asked 2021-03-11
Use the divergence theorem to evaluate
\(\displaystyle\int\int_{{S}}{F}\cdot{N}{d}{S}\)
, where
\(\displaystyle{F}{\left({x},{y},{z}\right)}={y}^{{2}}{z}{i}+{y}^{{3}}{j}+{x}{z}{k}\)
and S is the boundary of the cube defined by
\(\displaystyle-{5}\le{x},={5},-{5}\le{y}\le{5},{\quad\text{and}\quad}{0}\le{z}\le{10}\)
.
Second order linear equations
asked 2021-03-11
Solve the linear equations by considering y as a function of x, that is, y = y(x).
\(y'+2y=4\)
Laplace transform
asked 2021-03-11
Find the Laplace transforms of the given functions.
\(f{{\left({t}\right)}}={6}{e}^{{-{5}{t}}}+{e}^{{{3}{t}}}+{5}{t}^{{{3}}}-{9}\)
Conic sections
asked 2021-03-11
A solid is formed by cutting a conical section away a right circular cylinder. If the radius measures 6 in. and the altitude measures 8 in., what is the volume of the resulting solid?
Parametric equations, polar coordinates, and vector-v
asked 2021-03-09
Given
\(\displaystyle{r}′{\left({t}\right)}=⟨{\sec{{2}}}{t},−{\sin{{t}}}⟩\)
, find the arc length of the curve r(t) on the interval
\(\displaystyle{\left[−
Analysis
asked 2021-03-09
Error Analysis A student solved the equation 2cos θ = √2 for 0 ≤ θ < 2π and got θ = (π/4). What was her error?
Analysis
asked 2021-03-09
An investment program was set up using an annuity due with payments of $1,200 at the beginning of each quarter. Consider payments for 5 years are made into an account expected to pay 8% compounded quarterly. What is the amount of annuity?
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