Suppose f (x, y, z)= + P = (2, 4, 3). A. Find the gradient of f.

Q: Evaluate the integral and interpret it as the area of a region. π/2 15 sin x 5 cos 2x dx Sketch the…

A: Given integral :- ∫0π25sinx-5cos2xdx

Q: Find the intersection of the line r(t) = (1,0,−1) + t(4, 14, 2) and the plane x − z = 6. (Give your…

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Q: In Problems 43–46, the graph of a piecewise-defined function is given. Write a definition for each…

A: graph of the function is : This is a piecewise graph. The line which passes through the origin and…

Q: For the function f1x2 = x2 , compute the average rate of change: (a) From 1 to 2(b) From 1 to 1.5(c)…

A: Note:- Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Question Which of the following polynomials is guaranteed by the Intermediate Value Theorem to have…

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Q: -22 - x2, find f(x), f(x), f(x), and f(4)(x). " (x) 70 = aph f, f', f", and f" on a common screen. y…

A: Given query is to find indicated derivatives.

Q: Question 1; Part A,B,C Determine whether the following statement is true or false. True False If…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: State whether the equation is ordinary or partial, linear or non-linear, and give its order and…

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Q: Given f(-19) = -17, g(19) = 13, f'(19) = questions below: a) k(x) = 8f(x) - 4g(x) k'(-19) = b) k(x)…

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Q: y=tan(x/3) at x = 3

A: The function is given by y = tanx3 To evaluate: The value of the first and second derivative of the…

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Q: Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal…

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Q: Part A What average force is required to stop a 990 kg car in 7.6 s if the car is traveling at 87…

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Q: Fill in each blank so that the resulting statement is true.

A: Given, x+25

Q: what is odd function?

A: Function:- As a number of inputs with one output for each, a function is defined as a relationship…

Q: The graphs of a = F 3, y = f(x) (solid) and y = g(x) (dashed) are shown; the graph is not drawn to…

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Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

A: Given : Bernoulli's Equations 6y^2dx- x(2x^3 + y)dy = 0

Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: f(t)=−5t2−4t+5 Find f′(t):  Find f′(1): Find f′(2):

A: Given that  f(t) = -5t2 -4t +5 We need to find  (1)  f'(t)  (2) f'(1) (3) f'(2)

Q: Find the limit lim h->0 lim h→0 f(−11+h)-f(-11) h f(−11+h)-f(-11) h 0 if f(x)=1238 - 6x².

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Q: the solution of A=19 is incorrect. The answer was suppose to be A = 21 but I am not sure how that…

A: Graph:-

Q: Determine the equation of the plane containing the point and the line. (-7, 10,-3), r(t) = (1 - 4t,…

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Q: Differentiate the function:  y=1/x^5 y'1=

A: Given query is to find the derivative of the function.

Q: For the function graphed below, find the values of x at which the derivative does not exist. (Enter…

A: Given the graph of a function  f(x) . By using graph we need to find points where f(x) is not…

Q: dr Find giving your answer in terms of m. dr 1 x +4 3 Given that f 11 * calculate the value of m.

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Q: Calculus A kite 65 feet above the ground moves horizontally at a speed of 8 ft/s. At what rate is…

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Q: Consider the ellipsoid x² + y² + 4z² = 41. Find the acute angle that the tangent plane at the point…

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Q: How many 2-letter words can be made from the letters WASTEFUL if repetition of letters is allowed?…

A: How many 2-letter words can be made from the letters

Q: evaluate the definite integral that represents the volume of the solid formed by revolving the…

A: We have to write the definite integral for volume according to the given information then we have to…

Q: Find Duf at P. 1 f(x, y) = 3(1 + xy) ³/²; P(5,3); u= NOTE: Enter the exact answer. Duf = i+ 1

A: To find the directional derivative of given function.

Q: 4. ง √2t² - 3t+5-t+4 lim x-∞ √√3t² + 4t+1+t-2

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Q: 205. R dx x³ - 2x² - 4x+8 Et

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Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

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Q: 7. Write a formula for the triple product rule, the derivative of p(x) = f(x) · g(x).h(x)

A: Given query is to apply triple product rule

Q: Check if g is continuous at t=0 and t=1. If discontinuous, identify the discontinuity as remova

A: We find left hand limit and right hand limit of g at t=0 &t= 1 respectively. Then check the type…

Q: 8. DETAILS S - f*✓² The arc length function for a curve y = f(x), where f is an increasing function,…

A: Solution

Q: Find the linear approximation L(x) of the function ¹ƒ(x) = x² + 2x³ at a = -1.

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: The exercise involves observing a pattern in the expanded form of the binomial expression (a + b)n.…

A: Given data:- (a + b)1 = a + b(a + b)2 = a2 + 2ab + b2(a + b)3 = a3 + 3a2b + 3ab2 + b3(a + b)4 = a4 +…

Q: Given: x²y 01 02 00 O 1 | 2 dy dx = e³, Find: c if y = 0, x = 1 O None of the Choices

A: see below the answer and explanation with calculation

Q: If f1x2 = int12x2, find(a) f11.22 (b) f11.62 (c) f1 - 1.82

A: Given information fx =int2xorfx = 2x

Q: Let c be a constant and let f and g be differentiable functions on R². Use the gradient rules…

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Q: Question дz Find for z = cos (8xy). əx

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Q: -3 2 -1 8 7 * -12 ㅗ 2 + 3

A: Given graph:-

Q: Using the definition, calculate the derivative of the function. Then find the values of the…

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Q: For #9, 10, find and label an equation of the tangent line and an equation of the normal line to the…

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Q: Using Lagrange multipliers, find three positive numbers whose sum is 21 and such that the sum of…

A: Minimum value of sum of square is=147

Q: Find Duf at P. f(x, y, z) = 3x²y³z³; P(1, -1, 2); 2 2 -k 3 u +

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Find f' (1)

A: