z = (x + y)², x = s²t, y = st². Use the Chain rule to find dz ds for t= 1 and s = 2.

Q: 97. Σ n=1 1 2n(n + 1)

A: The given series,     ∑n=1∞12nn+1

Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

A: For a geometric sequence with first term a1 and common ration r is given by an=a1rn-1, for…

Q: At what points is the following function continuous? 5 cos 0 0+1 y = OA. The function is continuous…

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Q: Evaluate: 12+3 2√x+3 ○1-3 ln (7/5) O2-3 ln(7/5) 2 O2+3 ln7 03-In()

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Q: The function f gives the weekly profit, in thousand dollars, that an airline makes on its flights…

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Q: Use Newton's method to approximate a root of the equation 3x7 + 7x² + 2 = 0 as follows. Let 1 = 1 be…

A: Follow the procedure given below.

Q: State the domain of each function below in interval notation. 3x a. q(x) = 39 x+9 b. p(x) = 3x³x² +…

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Q: Use the given information to find the exact value of the trigonometric function.  sin θ = 1/4 , θ…

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Q: Integrate I -dz Select one: O A In 1-¹-2²+√1 − x² + C I OB. 21n1-¹³+√1 − x² + C | OC. In 1-²+√1 = z²…

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Q: (2x²-10a+15) da Integrate: f gở ba tô 2x+3 ln()+ +C n(²²³)+c +C 3 In O2a +3 ln()+ ○ 3 ln() + C o +C

A: We have to integrate ∫2x2-10x+15x2-5x+6 dx.

Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

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Q: Question 22 A square is increasing in area at a rate of 20 mm² each second. Calculate the rate of…

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Q: Calculate the integral where R is the region inside x ^2 + ?^ 2 = 4? and external to x ^2 + ? ^2 =…

A: We have to calculate the integral.

Q: Get the interval and radius of conv this given power series (x - 3)" n

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Q: A movie theater has a seating capacity of 163. The theater charges $5.00 for children, $7.00 for…

A: A detailed solution is given below

Q: Which of the following is a valid triple integral?

A: Which of the following is valid tripple integration

Q: Find the limit of the following sequence or determine that the sequence diverges. {tan - 1 (₁ -1…

A: Here we have to find the limit of a sequence.

Q: Use Newton's method to approximate a root of the equation 2 sin(x) = x as follows. 1 be the initial…

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Q: For the following exercise, use logarithmic differentiation to find dy dx y=xcotx

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Q: Which of the following is a valid triple integral? ⒸSS ſo ſh(e) (5) f(x, y, z) dzdydr h(y,z) flus) f…

A: We have to discuss about valid triple integral.

Q: The temperature at the point (x, y) on a metal plate is T(x, y) = Find the direction of greatest…

A:

Q: Farmer Jones and his wife, Dr. Jones, decide to build a fence on their farm. Because Dr. Jones is a…

A: Follow the procedure given below.

Q: 1. Find the domain of the vector function r(t) =< ln(t + 2), t 1 - 12 21 √12 - 4

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Q: A polynomial f(x) and one or more of its zeros are given. f(x)=x²-8x³ +95x² +16x-194 4-9i is a zero…

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Q: Use the Divergence Test to determine whether the following series diverges or state that the test is…

A: This question can be solved using the concept of divergence test.

Q: Find the angle of inclination of the tangent plane to the surface at the given point. (Round your…

A: Find the angle of incidence of the tangent plane to the surface of the given point.

Q: Solve the following initial value problem: y(t) = = dy dt +0.9ty = 6t, y(0) = 1

A: Given: dydt+0.9ty=6t,      y0=1

Q: EV None of the choices Ocot³ (1)-cot (1) - ○tan³ () - tan() Ocot³ (¹)-tan (1)

A: givenI=∫cot4(1θ)θ2dθlet  1θ=x-1θ2=dxdθ1θ2dθ=-dxI=-∫cot4(x)dx…

Q: 1 SSR (x+y)² dxdy

A:

Q: f the measurement of the side of a cube is increased from 5 cm to 5.2 cm, the approximate increase…

A: Side of cube is increased from 5 to 5.2

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³y³, P(8, 3),…

A: Here we have to find the direction derivative.

Q: The function w gives a person's weight t weeks after she begins a diet. Write a sentence of…

A: Since you have posted multipart questions. As per guidelines we"ll solve only first three parts.. If…

Q: Solve the following first-order linear differential equations. Simplify your answers. dy dt y = 0,…

A: We can answer the questions as below.

Q: Compute the given integral. Enter your answer using exact values. fe-52 dx = +C

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Q: Solve this system of equations x2+2y=0 -y2+2x=0

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Q: Evaluate: cot (9) -do None of the choices ɔ+ − ( 7 ) 400 - ( 7 ) 8400 O tan³ () – tan an ( 1 ) - + +…

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Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…

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Q: Find the gradient of the function at the given point. Function Point (3, 7, 2) f(x, y, z)=√√√√x² +…

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Q: Question 38 The critical point of f (x) = (sin x) (cosa) on the interval (0, π/2) is at x = Ono…

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Q: Given the function f(x, y)= xye+tan² esec2 y The second derivative fyy of f is equal to 0. Select…

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Q: Let f(x)=√6- x and g(x) = x² - x. Then the domain of f o g is equal to Question Help: Video Message…

A: Given- f(x)= 6-x f(g(x))= 6-x2-x f(g(x))= -x2+x+6 Domain of f(g(x))- -x2+x+6≥0 x2-x-6≤0

Q: A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate…

A: topic- application of derivatives

Q: What is the integral of f cos¹ (2t)dt? Ot+sin(4t) + sin(8t)] + C None of the choices cos" (2x)…

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Q: Question 25 A function has a relative maximum if O The first derivative test shows that the slope of…

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Q: Work problem 1 Consider the ellipsoid given by the equation: .8 53 - 5z². X + y 4 8 a) i ]Find the…

A: Let's find equation of tangent plane and normal line.

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: Integrate ze da Select one: O A. ex (2x-1) + C OB. e (x-2) + C O C. e* (x-1) + C O D. ex (x-3) + C

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Q: PART I. DIFFERENTIALS 1. √101

A: We can find the approximate answer as below.

Q: Simplify t to approximate the sum of the area using right end points. j=1

A: Given :fx=2x+40, 2    n=4

Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88).…

A: