Use the gradient to find the directional derivative of the function at P in the direction of v. h(x, y) = e-7x sin(y), p(1, 1), v=-i

Q: 2. Prove that f(x) = |x + 1] 1| (−1,0) tangent line at has no

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: A rate of change of H is given by Solve for k where H > -25. O 0.458 O 0.346 0.255 O 0.144 dH = k…

A: topic- differential equation

Q: Integrate (3-2)¹0 dar Select one: OA.(3-2)¹¹ +C OB.(3-2)¹¹ +C 12 OC.(3-2)¹¹+C OD.(3-2)¹¹ +C 10

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Q: Find the gradient of the function at the given point. In(x²-y)-3, (3,8) X Vz(3, 8) = z =

A: The given function,   z=lnx2-yx-3, at the point 3,8

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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: Integrate S 2x² (x − 1)(x² + 1) de using partial fractions.

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Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ |f₂(x, y) = O f.(x,y)= f₂(x, y) = 1…

A: We have to find derivative

Q: If f is a differentiable function and % up on Selected Answers: (0,1) f'(x)=x5 − 5x4+ 5x³+2, then…

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Q: Part b: We consider the function f(x, y) = x sin y - y cos x + y Find fx(x, y), fxy(x, y), and fxyx…

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Q: Differentiate implicitly to find the first partial derivatives of z. x In(y) + y²z+ z² = 93 дz əx дz…

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Q: If the given sequence is a geometric sequence, find the common ratio. 4/3, 8/3, 16/3, 32/3, 64,3

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. Identify an 8 Σ (-2)^…

A: Understanding of the ratio test is required in order to understand this problem.

Q: 8. Solve the differential equation: y' √x 7y

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Q: Evaluate the integral: CT/2 cos² (4x) sin³ (4x) dx.

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Q: Use Newton's Method to estimate a root of the function f(x) = x + 2 - e Use the initial estimate 1 -…

A: We need to find x7.

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

A: Given problem:- Find the normal vector of the tangent plane to the surface defined by…

Q: If the first 5 terms of a geometric sequence are {12, 6, 3, the formula for the nth term in the…

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Q: 3. A 20 ft ladder is leaning against a wall and begins to slide. How fast is the top of the ladder…

A: A 20ft ladder is leaning against a wall and begins slide.The ladder is 12ft away from the wall and…

Q: The differential equation dy 6x + 2 da 12y² + 14y + 5 Find such a solution and then give the related…

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Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

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Q: The limit: exists, and equal to 0 Select one: True lim (x,y)-(0,0) Falas x-y x² + y² The gradient…

A: Here we have to check whether the statement is true or false.

Q: The partial derivative fx(-1,0) of ƒ(x, y) = xe³ + x² + 1 is equal to −1. Select one: True False

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Q: Sdr Select one: O A. OB. O C. O D. (2x-1)³ V + √2x−1+C 3 +√√2r-1+C +√√2r-1+C + √√√2r-1+C (2z-1)³…

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Q: Evaluate the integral [x x cos x dx

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Q: 8. Use that (1+x)-2 = 1-2x+3x² - 4x³ + for -1 ≤ x ≤ 1 to find the first four nonzero terms of the…

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Q: 3) [ Consider the DE: -(4x³y - 16)dy = (6x²y² - 10)dx. A) Show that the differential equation is…

A: Given :-4x3y-16dy=6x2y2-10dx

Q: Find the solution of the following IVP: y(t) = = dy dt 2ty=9t²e, y(0) = 5.

A: We have to solve the given IVP.

Q: Find the power series representation of the following functions 3x (a) f(x) = 2x+7

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Q: A rectangle is constructed with its base on the diameter of a semicircle with a radius 18 and with…

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Q: u⃗=5i⃗−j⃗− k; v⃗=−i⃗+5j⃗+8k.  Find the projection of u ⃗ onto v :⃗

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Q: Which of the following is dž for t = 1 if dz dt 2t Z = In(x²y³), x = e¹ and y = e²¹ ? Select one: O…

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Q: QUESTION 5 Find the 2nd solution by reduction of order. y" - 4y +4y=0; y₁ = e²x

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Q: (hex) = (7x-6x³) 9 2) 3) x+1 x-1 x√x+1

A: Find the derivative

Q: 6. J 4 x4-1 -dx

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Q: -(4x³y - 16)dy = (6x²y² – 10)dx. A) Show that the differential equation is exact. B) Solve the…

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Q: Evaluate tan² (-a) se c5 (-a) da

A: Given problem:- ∫ tan5(-x) sec5(-x) dx

Q: random variables X and Y have the joint density f(x, y) = {1.5 (x² + y²),0 ≤ x,y ≤ 1, 0, elsewhere.…

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Q: Evaluate the following integral using the Fundamental Theorem of Calculus. Discuss whether your…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 11 -…

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

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Q: The value of the integral is: b 12 f(x) dx = a

A: Given that the graph of the function  To find the definite integral that represents the shaded area

Q: Consider the following. w = xy cos z, x = t₁ y=t5, z = arccos t (a) Find dw/dt by using the…

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

A: We have to find the 10th term. The general term geometric progression is given by- an=a1rn-1

Q: Find the directional derivative g(x, y) = x² + y², of the function at P in the direction of v. P(5,…

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Q: Calculus I Find d^2y/dx^2 for x + y^2 = 3

A: Solving the problem by finding the value of the problem.