nance. A person wishes to have $27,100 cash for a new car 4 years from now. How much should be placed in an account now, if the account pays 6.5% annual erest rate, compounded weekly?

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

A: Given problem:-

Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

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Q: 4) Find the critical points of the parametric equations x = t* – 1 y = t3 -t

A: Topic:- application of derivatives

Q: (5x2 – y²) dx + 2ydy = 0

A:

Q: Sketch the region R and evaluate the iterated integral (x, у) dA. - 2x + 8y) dy dx y y 2.0- 2.0- 1.5…

A: In this question, Firstly, we sketch the region and after that find iterated integral.

Q: For the function g whose graph is given, state the following. (If the answer is positive infinite,…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others…

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

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Q: It is known that dx Compute . Simplify the final answer. 2х-у dx

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point (2,…

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Q: Solve the following indefinite integrals, using substitution or integration by parts where needed 10…

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Q: 3 if x 2 the one-sided derivatives of f at x = 2 whether f' (2) exists. If it exists, specify its…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+ 5z'yk. ,62 div F= curl F=

A:

Q: Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America…

A: Given problem:- Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in…

Q: dx Ух — 12

A:

Q: 9.) A particle moves in a straight line according to the law of motion: s=cos(x). a. Find the…

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Q: Find f, and f and evaluate each at the given point. F(X, v) = arctan). (2, -2) f,x, y) = %3D X, v) =…

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Q: 2. Find an equation of the plane containing the point P(0, –,÷) and the line determined by the two…

A:

Q: A 25-year old woman burns 350 Gatorade is 55t calories during the tth hour. What is her net decrease…

A: A 25‐year old woman burns 350-60t cal/hr while walking on her treadmill. Her caloric intake from…

Q: Determine whether the improper integral diverges or converges. In x xp O converges O diverges…

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Q: Let F(t) = Find a parametric equation of the line tangent to F(t) at the point (111, 648, - 4.394)…

A: Let r→t=4t3+3, t5+5t4, -2 ln3tTo find the parametric equation of the line tangent to r→t at the…

Q: 1) What are the equations (4 of them) that show the relationship between polar and rectangular…

A: We can solve as follows

Q: Match the vector field with its graph. F(x, y) = yi y 1信 5 5 y 5 -6+ -5+

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Q: О а. 1.56 J ОЬ. 3.25 J Ос. 1.94 J O d. 2.33 J

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Q: The temperature at point (x, y) is given by T(x, y) = 100 – 3x² – y³. Find the direction from point…

A: Given

Q: 7) FIND EQUATION Of THE TANGENT AN LINE TO THE PARAMZTRIL X=t-+もt こe AT t =0. CURVE

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Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: 3 - (3x + 3ry')dx - (3y - 2y - 3xy)dy = 0

A:

Q: f(x) = (-3x³ + 4) 7, which of the following is f'(x)? f' (x) = 63x² (-3x° + 4)-8 - f' (x) = 63x(-3x…

A: Topic:- derivatives    Using  Derivatives of x^n = nx^(n-1)

Q: EVALUATE. 2022 a) x n (xl dx dx 2x+3x+7 dx (x+1) (x² +S)

A: This question can be solved by applying the concepts of indefinite integrals.

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: 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: Evaluate

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Q: Find the area between the loops of the limacon r= 7(1+2 cos 0). Area =

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Q: 2 2. Find an equation of the plane containing the point P(0, -) and the line determined by the two…

A:

Q: Given the function: x2-4 if x 2 f(x) = , 2-x if x = 2 What should be the value of k so that f is…

A:

Q: Given y = (x + 1)(x + 2)² Find: y O (z + 2)(3x – 4) O (2 – x)(3x – 4) - O (x – 2)(3x + 4) O (2 +…

A: Apply the product rule of differentiation f·g'=f'·g+f·g' to find the derivative of the given…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: 5 4 3 1 -1 T/2 3T/2 -2 -3 - -4 -5 The graph of the function f(x) = csc x is given above for the…

A: The graph of the function fx=csc x is given for the interval x∈0, 2π. We have to find one-sided…

Q: (3x-3) dx (x²-2x+1)(x²+2x+8)

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Q: The cumulative percent of sexually active boys ages 15 to 20 is given in the table. Complete parts…

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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: The temperature at point (x, y) is given by T(x, y) = 100 – 3x² – y³. Find the direction from point…

A: Given :

Q: /hat is the area of the region bounded by the graphs of æ = y³ – 2y and DA = (3x – x² )dx DA = (? –…

A: Topic:- application of integration

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A: Given

Q: (2x – 3y) dx + (2y – 3x) dy

A:

Q: Find div F and curl F if F(x, y, z) = 3y°z©i – 3x*z°j – 3xy*k. div F= curl F=

A:

Q: Find div F if F(x, y, z) = (x² + y) i + z² j + (ey - z) k. 2x - 1 O 2xy i +k O 2x i -k 2хy - 1

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Q: alluse The g auss elemina fion to find the 2. -3 2. -2

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Q: Evaluate the improper iterated integral. 9. x2 dy dx 1 + y?

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Q: 12 dx х3 — Зх2

A: