5. (8 pts) An isosceles right triangle is as shown in the figure. The leg is increasing at a rate of 1 ft/s. When the area of the triangle is 8 square feet, at what rate is the hypotenuse increasing? Use the very symbols on the figure, and do not use any calculator. X X y

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A: Explanation of the answer is as follows

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Q: Evaluate the integral. [8 sin √xdx Ja sin √xdx= 8

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Q: Translate into English:  a. ∀x(E(x) ⇾ E(x + 2)).  b. ∀x∃y(sin(x) =y).  c. ∀y∃x(sin(x) = y).  d.…

A: Solution : Given that to translate into English

Q: B: e²+² dydx Jo Jo

A: To solve the integral ∫0∞ ∫0∞ ex2+y2dydx

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A: Aim:- To calculate : ddx(au)

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A: We have to find the partial derivative.

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A: If fx, y=x2+y+4, then to find ∂2f∂x2 and ∂2f∂y∂x.

Q: (c) Given a cubic function i) Find the critical point(s). ENTIA ii) Hence, determine the maximum and…

A: Let's solve.

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A: We have given a function and finding point for local minimum value

Q: Let à (6, 7, 4) and 6=(3,2,2). = (a - b) × (a + b) i

A: To find cross product.

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A: Follow the procedure given below.

Q: X √I + X dx

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Q: 7. Show that the equation f(x, y) = sin(x + y) + cos(x - y) satisfy the wave equation 0²1 a³f dx²…

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A: We can find the answer using the data given in the table as below.

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A:

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A: See this solution in below

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A: You must have idea how to find solution for differential equations.

Q: Question 2 Consider the point P(-2, 1, 4) and the vectors a = and b=. (a) Find the unit vector u…

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Q: bounded by the curve. Find the area y=2x+₁²₁ y=10x-x²

A: Given:  the curve is y=2x+12                               y=10x-x2

Q: Evaluate the indefinite integral. x² A -dx 1- x6

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Q: Given i) Find the values of x and y when t = 3. the va Find dy E dx RAL LWhen IMA nd when 123 CALC…

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Q: Question Which of the following is a potential function f for F(x, y, z) = (2x cos(v2). -x²z sin(yz)…

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Q: X = [₁,√38² - 1 db y = v √314 - 1 dt, -2 ≤x≤-1

A: Firstly find  derivative of y then find length of curve

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A: Here is the solution:

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Q: f'(x) = x²¹ - 2x² x¹2x² 2x−² + 1; f(1) = 5

A: Given that f'(x)=x-1-2x-2+1 -(i)Also given that f(1)=5.Our Aim is to calculate the antiderivative of…

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A: Use disk method

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A: NOTE: Refresh your page if you can't see any equations. . the given equation is take derivative

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Q: The Taylor series expansion of 2 |z| < 1 is (solve) Z-2¹ −(¹ + ² + ² + ² …..) X Option 2 O…

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