1. Use the Chain Rule to find 1. y = u² + 1 dy dx (show your complete solution) . u = x² - 1

Q: Əw ax Find a. y dw ax (-1, -2,2π) a. and b. = Əw at the point (x,y,z) = (- л₁ − 2,2µ) if w = x² + y²…

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Q: Evaluate the following integrals: 4x 6. ²x3x²y²dy dx 7. p² sin 0 d0 dp Ꮎ dᎾ π/3 π/6 8. (2-y)dy dx 9.…

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Q: Consider the differential equation 2xy" - 3y + 3y +³/4 = 0 (1) It turns out that y₁ = r is a…

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Q: 2. S dx x²-x+2

A: Given problem:-

Q: yields y'= 38263752. This means that when x-6 the function y: A) Decreases at the rate of 4782969…

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Q: Y y=√√√1-x² x Show that the volume under the surface z = 5x²y over the half of the unit above the…

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Q: Determine the intervals on which the function is concave up or down and find the points of…

A: solution:-f(x)=6x3-11x2+1f'(x)=ddx6x3-11x2+1=18x2-22xf''(x)=d2dx26x3-11x2+1=36x-22

Q: y = ln 1-x² 1+x²

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Q: Q4: A- Find the flux of the field F=- i+j+k √√x² + y² +2² bounded below by the plane 2-0 and bounded…

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Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: Which value of c satisfies the conclusion of the MVT for the function f(x) = -6x²-3x - 2 on the…

A: Solution-

Q: Determine the intervals on which the function is concave up or down and find the points of…

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Q: 3. Apply the three conditions of continuity to determine if the function f(x) = 2x²+5x+2 x²-x-12 is…

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Q: S 2+2 cot (2²+42 - 3) -dz

A: Solution of given question is written in below steps.

Q: Let f(x) f'(x) find the values of A = B = C= D = 1 3x4+x3 + x -5 x3 -5.5 - X + 13.2 = (2AB-1 Given…

A: The given function is: f(x)=3x4+x13+x-5x3-x-5.5+13.2

Q: et R be the region below bounded by the parabola y and y = 0. (0,4) (1,3) R (-2,0) (-1,0) x and the…

A: definite integral

Q: In the following problem, begin by drawing a diagram that shows the relations among the variables.…

A: Use partial derivatives

Q: The population of a small city is 90,000. 1. Find the population in 20 years if the city grows at an…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: 3. (x² - y²) dx + xy dy = 0

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Q: Scoth (2) dx

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Q: Consider the matrices shown below: A [閒 Compute tr((CTB)AT) 25

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Q: 8) Maximize the function f(x, y) = 16-r² - y² subject to the constraint x + y = 6

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Q: The proper way to evaluate f(x + h) for the function f(x) = 3x²-x+4 is f(x + h) = 3(x+h)² - x +h+4…

A: Topic:- function

Q: 5. √√64 .05

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Q: Find the area of the region above the x-axis bounded by the function y = 4x - x2 – 3

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Q: If g(x) = (ax² + x) (ax - 1) for some real number a, find lim g(x). x→1 00 O (x²+x)(x - 1) The limit…

A: Find the limit

Q: In 2000, an investment was opened with an initial deposit of $1800. The investment had grown to…

A: We have to find the formula and time.

Q: f(x) = 9x² - 4 at x = 1

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Q: Solve the DE by Integrating Factors Found by Inspection 3 1. x dy - y dx = x¹ y dy + x³y² dx X

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Q: 4 2 dx 5₂ is same as evaluating lim cos-¹(f(x)). Determine the value of f(x) if x√√x²-4 c→ 2+ Add…

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Q: D in one polar plane, plet the following points a.) (4, π/3) bi) (-3, - STT) d.) (21-77) 4 e) (-1.5,…

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Q: ex V1-e2x 1. S dx

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Q: 1. 3) Suppose A = 4i-6j, B = i + 7j and C = 9i - 5j. Find (a) ||5B-3C|| (b) unit vector having the…

A: Given: A=4i−6j, B=i+7j and C=9i−5j Since you have posted a question with multiple sub-parts, as per…

Q: Solution 1 y = (x +3)(2x – 5) y = 2x² + 6x - 5x - 15 y = 2x2 + x - 15 y = 2(2x)2−1+1-0 y' = 4x+1…

A: Please see the below picture for detailed solution.

Q: y" + y = 3x sin x

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Q: Find the area bounded by the parabola y2= 4x, the x – axis and the lines x=1 and x=3.

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Q: (ylny − e¯xy)dx + ( + xlny) dy = 0 -

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Q: 2. Use geometry to evaluate (2 (2x+6)dx. You need to draw a graph.

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Q: Let f defined by f(x) = 2x³ + 3x² − 5 at [-1,1], Consider the following statements 1-It reaches an…

A: The given function,   fx=2x3+3x2-5 at -1,1

Q: 7 H W N r 1 9 na O 1 2 3 4 5 According to this graph, the function is discontinuous at x = 2. True…

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Q: Determine if the series converges or diverges Sum n=1 (n+1)/(n+3) State the test used, show that all…

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Q: 'ind R(t) given R(1) = (1,0,−1). 'ind f'(1) if f(t) = (-2, -3t, t²). R' (t).

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Q: n = 3 20 . n=-1n+₂

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Q: Directions: Give the answer completely. Show the graph and the plane region in the Cartesian plane.…

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Q: 6. a) Find the critical value(s) of f(x) = x + 2sin(x) on the interval 0≤x≤ 2π 3 b) Classify each…

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Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

Q: Directions: Using Fundamental Theorem of Calculus (FTOC), compute the following definite integrals.

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Q: 1. x² - 2xy + y² − 6x + 2 = 0

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Q: Find the maximum value of f(x,y) = 26-x² - y² on the line x + 4y = 17. The maximum value of f(x,y) =…

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Q: Find the maximum and minimum limits of the function X-2 (x + 2)²

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