10e²x When x = 0, y = 0, y' = 0 9. (D2+1)y= Ans: y=-2 cos x-4 sin x + 2e2x

Q: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: Let f(x, y, z) = n(4xy) + sin(xy² + ye*). Find fayz.

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Q: Find an antiderivative F(x) of the function f(x) = 5 sin(x) such that F F(7) 2 F(x): Now, find a…

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Q: Question 8 (a) Find the following integrals: 1 (1) √4x²+0 d 6 (ii) -dx -2x-8

A: (i). Given: I=∫14x2+9dx   ...1   As we know that; The trigonometric identity; 1). tan2x+1=sec2x 2).…

Q: (b) Find the area under the curve defined parametrically as x=t²-1 and y=t³-t for 0≤t≤1

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Q: Q1: If the function f(x) define as f: R→ R such that f(x)= (x+1, x> 2 x²-1, x≤2 Show that the…

A: To show that function f is differentiable at point x=2

Q: 3. Find the area of the region bounded by the graphs of y = 2 - x² and y = -x. 4.5 O 1.5 O -1.833…

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Q: 1. 2y7y"+12y + 8y = 0

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Q: Test the equation below for exactness. If exact, solve. If not, use an integrating factor (find it…

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Q: B. Solve the following integrals. 2.) fevdxdy

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Q: Solve the initial-value problem. x' + 7x = e-7t x(t) =| X cos(t), x(0) = -1

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Q: Use linear approximation to approximate the value of 65 without the need for a calculator.

A: This question can be solved using the concept of linear approximation.

Q: Find the tangent line approximation for √1+ x near x = 5. y = ||

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Q: When multiplied out, what are the first 4 terms of (2x+y)¹0? Show your work for full credit.

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Q: 2 ( D° _ 2D - 20 - 3D - 2) y = 0 = 9

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Q: Consider the function f(x) = 4sin(pi/3(x-2) + 8  what is the maximum and minimum y values and their…

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Q: Calculate the value of the line integral fds where f(x, y, z)=e² and C is described by X C (x, y,…

A: The objective of the question is evaluate the definite integral.

Q: AY (1, 1) A X=1 y=x² с X (0,0) = 1, and the y-axis. Region A is bounded by the parabola x = y², the…

A: Note : As per our guidelines we are supposed to answer only 3  subparts if there are multiple…

Q: An object is moving with velocity (in ft/sec) v(t) = t²-2t + 3. At t = 0, the object has a position…

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Q: The linearization a at a = 0 to √8+7x is A + Br. Compute A and B. A B=

A: To Find: Linearization for fx=8+7x at a=0

Q: Given the points A = (1,-2, 3) and B = ( 3, 4, -1), find the following:

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Q: (b) ₁₂ (x − 1)(x + 2) de L dx - -2

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Q: A poster of area 6000 cm² has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the…

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Q: its not 1

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Q: Applications of Differential Equations 3. A small metal bar, whose initial temperature was 20° C,…

A: Above question is solved.

Q: Find the tangent line approximation for √1 + x near x = 5. y = |

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Q: What is the 100th term of the sequence –3, 2, 7, 12, ...?

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Q: Find an antiderivative F(x) of the function f(x) = 2√√x + 4 such that F(0) = - 7. F(x) Now, find a…

A: Given: (a). fx=2x+4   As we know that; The Power rule: ∫xndx=xn+1n+1+C And The expression for the…

Q: Find the length of the curve Arc length = UT → y² = 4x, 0≤ y ≤ 2.

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Q: Find the derivative of y= 25 + 14.

A: Topic = Derivative

Q: a.) Show that an is a perfect square where the sequence {an) is defined recursively by an+2 =…

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Q: If z₁ = 5-i, z₂ = 1-2¡ then evaluate 32₂ +22₁-5- z, 2z, -3z₂ +3-i

A: Use complex number concept

Q: 2. A basketball is being filled with air at a rate of 6 in /sec. (You can assume the basketball is a…

A: Given change in volme dV/dt= 6in3/sec Radius of ball is r= 1in then diameter   d= 2in Formula:…

Q: The arc length of 元 y=ln(cos x), 0<x<= is 3 the curve

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Q: Q2: dy du (A) Show that if y=csc(u), then -csc(u) cot(u) dx dx

A: SOLUTION-

Q: Carbon Monoxide Pollution The number of cars running in the business district of a town at time t is…

A: topic - composite functions

Q: Is it possible to get the area between y² = 3x and y = x³, using a. vertical strips b. horizontal…

A: Area between curves

Q: 4. h(x, y) = xe +y+1

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

Q: Which of the following is not an indeterminate form? * ∞-∞ O Option 1 0/0 O Option 2 1∞ 1/0

A: Topic = Limits Correct option = 4

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t + 32) sin(t)dt

A: We can evaluate the given integral by using the tabular integration.

Q: An oil storage tank can be described as the volume generated by revolving the area bounded by 4 Y =…

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Q: PLEASE ANSWER:  Find the number in the interval [−1, 1] such that the sum of the number and its…

A: To find the number in the interval [-1,1] satisfying the given conditions.

Q: Calculate the partial derivatives at (T, U, V, W) = (4, 1, 5, 10). (Use symbolic notation and…

A: We can find the partial derivative of the given expression .

Q: 10. f(x, y) = x/(x² + y²)

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Q: a) Approximate the area under graph (a) of f(x) = 2/x² over the interval [2,6] by computing the area…

A: Area using rectangle

Q: * 37 015) 15/(x)=x+cosx, xe[0, z], then the function has an inflection point at x A)- 110) C D) # 2…

A: Asked questions are solved.

Q: Evaluate the following integral: * *π/2 [sin² 6 1/42 4 O - (2/63) O - (3/28) O 2/63 sin x cos³ x

A: The objective of the question is evaluate the definite integral and choose the correct option.

Q: 5. By considering the derivative of the function f : [-1,-1] → R defined by f(x) = show that f-¹…

A: Concept: inverse function: An inverse function, sometimes known as an anti function, is a function…

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by 3 L(x,y) = x²…

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Q: local linear (20) 1f the graph of the function f(x) is stretched vertically by a factor 2 and then…

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