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# Recent questions in Multivariable calculus

Multivariable functions
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asked 2021-06-26

### Let $$\displaystyle{f{{\left({x}\right)}}}={5}⋅{2}^{{x}}$$ a. Write an equation for p, the parent function of f. b. Give the equation for an asymptote of both p and f.

Multivariable functions
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asked 2021-06-08

### Write formulas for the isometries in terms of a complex variable $$z = x + iy.$$

Multivariable functions
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asked 2021-06-03

### Let f1,…,fr be complex polynomials in the variables x1,…,xn let V be the variety of their common zeros, and let I be the ideal of the polynomial ring $$R=C[x1,…,xn]$$ that they generate. Define a homomorphism from the quotient ring $$\overline{R}=R\ x2F$$; I to the ring RR of continuous, complex-valued functions on V.

Multivariable functions
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asked 2021-03-18

### Use Green's Theorem in the form of this equation to prove Green's first identity, where D and C satisfy the hypothesis of Green's Theorem and the appropriate partial derivatives of f and g exist and are continuous. (The quantity grad g · n = Dng occurs in the line integral. This is the directional derivative in the direction of the normal vector n and is called the normal derivative of g.) $$\displaystyle\oint_{{c}}{F}\cdot{n}{d}{s}=\int\int_{{D}}\div{F}{\left({x},{y}\right)}{d}{A}$$

Multivariable functions
ANSWERED
asked 2021-03-02

### COnsider the multivariable function $$\displaystyle{g{{\left({x},{y}\right)}}}={x}^{{2}}-{3}{y}^{{4}}{x}^{{2}}+{\sin{{\left({x}{y}\right)}}}$$. Find the following partial derivatives: $$\displaystyle{g}_{{x}}.{g}_{{y}},{g}_{{{x}{y}}},{g{{\left(\times\right)}}},{g{{\left({y}{y}\right)}}}$$.

Multivariable functions
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asked 2021-03-01

### Use Green's Theorem to evaluate $$\displaystyle\int_{{C}}\vec{{{F}}}\cdot{d}\vec{{{r}}}$$ where $$\displaystyle\vec{{{F}}}{\left({x},{y}\right)}={x}{y}^{{2}}{i}+{\left({1}-{x}{y}^{{3}}\right)}{j}$$ and C is the parallelogram with vertices (-1,2), (-1,-1),(1,1)and(1,4). The orientation of C is counterclockwise.

Multivariable functions
ANSWERED
asked 2021-02-27

### Evaluate $$\displaystyle\int_{{C}}{x}^{{2}}{y}^{{2}}{\left.{d}{x}\right.}+{4}{x}{y}^{{3}}{\left.{d}{y}\right.}$$ where C is the triangle with vertices(0,0),(1,3), and (0,3). (a)Use the Green's Theorem. (b)Do not use the Green's Theorem.

Multivariable functions
ANSWERED
asked 2021-02-22

### Write formulas for the indicated partial derivatives for the multivariable function. $$\displaystyle{g{{\left({x},{y},{z}\right)}}}={3.1}{x}^{{2}}{y}{z}^{{2}}+{2.7}{x}^{{y}}+{z}$$ a)$$\displaystyle{g}_{{x}}$$ b)$$\displaystyle{g}_{{y}}$$ c)$$\displaystyle{g}_{{z}}$$

Multivariable functions
ANSWERED
asked 2021-02-22

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