# Here's what students ask on Calculus and Analysis

### to what property does (-6 + 3 ) + 1 = -6 + (3 + 1) belong to

Multivariable functions

### 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

### Determine $$L^{-1}\left[\frac{(s-4)e^{-3s}}{s^2-4s+5}\right]$$

Laplace transform

### The simplified form of the expression$$\displaystyle{\sqrt[{{3}}]{{a}}}{\sqrt[{{6}}]{{a}}}\ \text{in radicalnotation is}\ \sqrt{a}.$$

Transformation properties

### 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

### 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

Integrals

### 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

### $$\displaystyle{y}'={6}\frac{{x}^{{2}}}{{{2}{y}+{\cos{{y}}}}}{)}$$

Differential equations

### Solve the linear equations by considering y as a function of x, that is, y = y(x). $$y'+2y=4$$

Laplace transform

Conic sections

Analysis