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Q: Activity 1.5.2. A potato is placed in an oven, and the potato's temperature F (in de- grees…

A: Solution: Given data

Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given problem:-

Q: Find the first partial derivatives with respect to x,y and z. f(x. y.z) - 3x°y - 9 xyz + 10 yz %3D

A: Find first partial derivative

Q: Evaluate | (2x – y) dx + (x + 7y) dy. C: x-axis from x = 0 to x = 8

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Q: Find the exact length of the curve given by z = t° , y = t (0 <t< 4). Length

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Q: Given the vectors A = 3i – 5j + 2k and B = 7i + j – 2k. Find the vector projection of A onto B.

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Q: Verify Green's Theorem by evaluating both integrals y? dx + x2 dy dA ду for the given path. C:…

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Q: xe 1. lim, »o X→0 1-e*

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Q: What is the equation of the plane that is tangent to the graph of z = x coS y – ye“, when (x, y) =…

A: Equation of the plane tangent to the surface z=f(x,y) :               Let   F(x,y,z) =0 ,then…

Q: Where is the function f(z, y) = In ( + arctan(y + z)) continuous? Lütfen birini seçin: a.{(x, y) €…

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Q: Find the integral of your answer in problems 2a and 2b. Note: My answer on 2a and 2b will be found…

A: Here we have to find the area.

Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. (x?2 - х) dx x2 + x +1

A: ∫01x2-xx2+x+1dxit is a improper fraction ( degree of Numerator= Degree of denominator)Using long…

Q: 3) Consider the curve parameterized by x = csc t, y = cot t, 0 < t < t. Determine the equation of…

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: a) Determine the intersection points. b) Draw a sketch of the graph. c) Find the area of the region…

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Q: Evaluate sin 5x) lim, 0 (sin 5z ) 3x O 1 O 3/5 O 5/3

A: Topic:- limit calculus

Q: Exercises: Find the derivatives of: 1. 1-y = (secx + tanx)(secx- tanx) 2- y = x2.cotx- x2 4. 1+cscx…

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Q: Determine whether each of the following functions is (a) continuous (b) differentiable 3. f(x) = v2…

A: If function 'f' is differentiable at x=c the f'(c) is the slope of the tangent of the function at…

Q: Use the following series in determining the IOC and ROC. The summation of [(7^n)/(n+5)](x-4)^(n+2)…

A: Given  problem:- Use the following series in determining the IOC and ROC. The summation of…

Q: cos(2x)– cosx sin x 4. lim, »o

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Q: Solve following diffrential equation x(dy/dx)+6y=9x^2

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Q: The outside diameter of a thin spherical shell is 12 feet. If the shell is 0.3 inch thick, use…

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Q: Find the extrema for F(x) = x*/x+1 on the interval [-l]

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Q: 1) Find and of the following equation then simplify whenever possible. dx x = 2u* – u3 + u – 11 , y…

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Q: Show that the differential form in the integral below is exact. Then evaluate the integral. (-2,4, -…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0<ts 1. (y – x) dx +…

A: Just I have used the given parametric representation of the curve C to change the given line…

Q: In(2+x) lim, x+-1 X+1

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Q: Evaluate the following: 1. S(x3+ 3x?)dx

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Q: Find the first three nonzero terms in Maclaurin Series for each function

A: This is a problem related to series expansion. based on the general formula of maclaurin series we…

Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the…

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Q: ||r'(t) × r"(t)|| ||r(t)||³ Use the formula k(t) to find k(t). r(t) = 2 cos(4t)i+ 2 sin(4t)j + 9tk…

A: We have to solve k(t)

Q: Find the equation of the tangent line to the graph of y = -2x° + 6x? – 5x + 10 at the point (1,5) in…

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Q: | (2x - y) dx + (x + 3y) dy. Evaluate C: arc on y = x5/2 from (0, 0) to (4, 32)

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Q: Q4. Find guerel polution of following systens uning either method' of undetermind coefticients or…

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Q: What is the angle between the vectors u = and v = ? 213° O 188° O 111° 120°

A: Solution:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4…

A: Given problem:-

Q: n 1) Use the Integral Test to determine whether the series is convergent or divergent. n² +1 n=1…

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Q: A ball is thrown upward from a height of 9.1 m at an initial speed of 42 m/sec. Acceleration…

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Q: Find T(t) and N(t) at the given point. r(t) = 11 cos(t)i + 11 sin(t)j + tk; t= -11 /122 T(5) V122 0,…

A: Given: r(t)=11cos(t)i→+11sin(t)j→+tk→ r'(t)=d11cos(t)dti→+d11sin(t)dtj→+dtdtk→…

Q: e. Suppose someone claims that C'(5000) = -0.1. What would the practical mean- ing of this…

A: We have to find the meaning of C'(2000).

Q: Determine whether the improper integral diverges or converges. -6x dx O converges O diverges…

A: This is a problem related to indefinite integral. Based on the general formula and concept we will…

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

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Q: 6 foND THE EXACT LENGTH Of THE zt -2t PARAMETRIL y(e)=1+4t CURVE X= e te

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Q: 3. If dt , find g'(2). 5. g(x) =

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Q: E1 Fnd all of the Porst order partial derivatives Toll wing fanctions. a)そ= x+5y x Sin (y). b) fexy,…

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Q: Find curl (8z i + 9x j+ 8y k). curl (8z i + 9x j + 8y k) i )i + ( i )j + ( i )k

A: Given that,     8z i+9x j+8y k

Q: Refer to the graph below. Find lim f(x). 3. 2- 1+ -5 4-3 -2 -1 -1+ 3. 4 5 x -2+ -3+ Does not exist 4…

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Q: Calculus

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Q: Using an appropriate substitution, cos x-sin x the integral 3. dx equals: 0 cosx+sin x O none of…

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Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. π 1 sin -x cos? 1

A: