8. Determine the dot product of u = [5,-3,1] and v = [2.–2,

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A: To solve the problem we use chain rule of derivative.

Q: g(x)=√(x² - 1)², find g'(x) O none of these answers O (2/3) (x²-1)-1/3.2x O (2/3) (x²-1)-1/3 O (2/3)…

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Q: The graphs of f and g are given. Use them to evaluate each limit, if it exists. (If an answer does…

A:

Q: 15. S sin²a da

A: The given integration is: ∫0∞sin2α dα  To evaluate the integration.

Q: 8. Water runs into a conical tank at a rate of 8ë ft³/min. The tank stands point down and has a…

A:

Q: 3. Consider the function f: (-π/2, π/2)→ R defined by f(x) =tan(x). A. The function f is injective.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the indefinite integral. (Use C for the constant of integration.) 2t 1 - 4t dt

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Q: let f(x)= 3x² -1, find [ (f(x+h)-f(x) ) /h] O 6x+3h O 6x² +6x-2 +3h O none of these answers O6x-3h

A: See the details solution in below

Q: 2 Let A = [3 and B matrices A and B commute? None a -4 For what values of a (if any) do

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Q: Use inverse matrices to find the solution of the system of equations. X + y + 2z = 7 2x + y + 2x +…

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Q: f(5) = 4 f'(5) = 2 g(5) = 1 g(5) = 4

A:

Q: Consider the Cobb-Douglas production function f(x, y) = 900x5y when x = 5000 and y = 2500. (Round…

A: The Cobb-Douglas production function,fx,y=900 x0.5 y0.5when x=5000 and y=2500.

Q: Q17 The sum of the arithmetic series: 8, 20, 32, 44,.. when n = 10 is equal to Q18 Fill in the Blank…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: Discuss the continuity of the function. f(x, y) = 1 - cos(x² + y2) x² + y² continuous everywhere…

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Q: f(x) = √√√x + 3 and g(x) = of 2: Find the formula for (gof)(x) and simplify your answer. Then find…

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Q: 4 2. The volume of a sphere with radius r is given by V = (a) Take derivatives of both sides with…

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Q: the full answer wasn't shown in the solution box, please provide the rest

A: any differentiable function must be continuous at every point in its domain so  a.) If a function is…

Q: Let f(x,y) = 3x^y + 4xy³. Find 224 224 224 224 2' ахду' дудх and ду 2' ах

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

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Q: 31. f(x, y) = √4 - 4x² - y²

A: We need to solve question (31) as student has specifically asked for the solution of it.   We need…

Q: What is the amplitude and phase shift of the equation (1)=0.3cos31+0.2sin3r? O O O A= O A= A= √13 10…

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Q: The owner of a video store has determined that the cost C, in dollars, of operating the store is…

A: The cost function give in the question is C(x)=2x2-26x+620

Q: KINDLY RESOLVE THIS PROBLEM! BOX THE FINAL ANSWER.

A: Given :

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Q: dw dt t Use the Chain Rule to find where w=cos 12x sin 2y, x=- S dw dt (Type an expression using t…

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Q: Evaluate the following integral. 5 dx secx-1 Simplify the integrand so that the denominator consists…

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = x4 -…

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Q: Questions 12-15: Determine if each series converges or diverges. Indicate which test you are using…

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Q: You invest $2,540 at a rate of 7.8% with continuous compounding. How much will you have after 7…

A: invest amount is $2540rate is 7.8%time=7 years formula for compound continuous is A=Pertwhere A is…

Q: Suppose that f(x, y) = 3x + 2y at which −1 ≤ x ≤ 1, −1 ≤ y ≤ 1. Absolute minimum of f(x, y) is…

A: We have the function f(x,y)=3x+2yAnd the domain is -1≤x≤1,-1≤y≤1.

Q: Evaluate the integral: int1/(x sqrt(9+x^2)) dx (A) Which trig substitution is correct for this…

A: Here we will use trigonometric substitution to solve the integration.

Q: . 3 = 2x= ܐx dx

A:

Q: at is the average rate of change between x-2 and x-3 for the function g(x) = 4(x + 1)² -5

A: Given query is to find the average rate of change.

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. -√x…

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Q: 2-0 3. Let f(x) = 2x³+4x-4. Use the intermediate-value theorem to estimate the location of the zero…

A: Given: f(x) = 2x3 + 4x - 4  Interval: [ 0 , 1 ]

Q: +(1+3) sin.xdy = 0 34. cos x dx + 1 +

A:

Q: A 17-ft ladder is leaning against the side of a house. The top of the ladder is sliding down the…

A: Given  length of ladder = 17 ft

Q: Use the chain rule. If y = √u and u = x2 + 11, find dy dx 11 dy dx

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Q: f(x) = (3x² -2)5, find f '(x)

A: Here we have to differentiate the function.

Q: do you know how to solve question 10 and 11?

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Q: Let f(x,y) = 5x²y + 3xy³. Find a²fa²fa²f a²f ах ду ?хду дудх 2' 2' 1 and

A: Partial Derivative

Q: Use the definition of continuity and the properties of limits to show that the function is…

A:

Q: could you actually show the work for the answer?

A: Given that,the equation of the tangent line to fx at the point a=1 is y=7-2x.We need to find the…

Q: A crew working with dynamite to clear a road blasted a large rock straight up into the air with an…

A: Velocity is given by ÷ vt=ddtst vt=ddt-16t2+170t vt=-32t+170..........answer a)

Q: The volume, V, of a sphere in terms of its radius, r, is given by V (r) = 7³. Express r as a…

A:

Q: Find both first partial derivatives. h(x, y) = e-(x4 + y4) hx(x, y) = hy(x, y) =

A:

Q: 60 For a monopolist's product, the demand equation is p = 29-4q and the average-cost function is…

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Q: . h(x) = x² +5, x³, x < 2 x ≥ 2; x = 2.

A: Given query is to find function is continuous or not at x = 2.

Q: Evaluate the indefinite integral. cos (3x) sin³ (3x) dx =

A: We need to evaluate the following integral I = ∫cos3xsin63xdx                            .........1