2. Find the general solution o- = y(1+e³) 1 له 342433434 11 11 1 "싫

Q: 1. Consider the differential equation y" - ry - y = 0 a) Determine two linearly independent power…

A: answer is in next step

Q: dy dx 11 - 4xy, when x = 0, y = 2

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Q: Find the binomion coefpicient (7)

A: follw the procedure given below.

Q: 1 s¯¹(x) 2 cos √1-x² -dx

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Q: Question B2 Consider the vectors, 3 p= and q= 2 (i) Compute 3p - 5q. (ii) Find the length of p, that…

A: A detailed solution is given below

Q: (4) Σ=o (−1)n+7 n2+3 1/1

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Q: Evaluate x³ dx (x4-5)4

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Q: Consider the function 2r²-9r-18 f(r) r²-r-2 (a) Sketch the curve y = f(r). (b) Find the area of the…

A: Here we have to find the area under the curve

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Q: Find the derivative of the function using implicit differentiation.  1.) x³-3x²y+2xy²=12 2.) x²-y²…

A: This question is related to implicit differentiation, We will solve it using given information.

Q: Use the series to evaluate the limit tan-¹ y - siny lim y→0 y³ cosy

A: Expand series and solve

Q: 4.) Sketch the graph, not by plotting points, but by starting with a standard function and applying…

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Q: What is the solution of 5 |x - 2|dx

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Q: A lighthouse L is located on a small island 2 km from the nearest point A on a long straight…

A: A lighthouse L is located on a small island 2 km from the nearest point A on a long straight…

Q: (-2, 39) 4 10 10 20 10 10 -20 30 40 1 (14) (27) 3 B. Locate and classify the critical point of y =…

A: The equation of the curve is given by , y=23x3-2x2-6x+2Now, We will apply the second derivative test…

Q: dy 5. Use Implicit Differentiation to find dx a) 4xy + x² = 4 - Iny³

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Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

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Q: 5. Determine whether the following statements are True or False? y = f(x) 2 X 0 (a) lim f(x) = 1 (b)…

A: Given graph of y= f(x)

Q: Consider the functions z= - ex In y, x = In (u cos v), and y = u sin v. dz əz (a) Express and as…

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Q: Consider the functions z= - ex In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and as…

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Q: Find the Area under a curve y = 4-x² from x = -3 to x = 3

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Q: 2 x (1 + y²) dx -y (1 + 2x²) dy = 0

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Q: 1. Evaluate the given integral Q. Q a = 1₁² 1₁² ² (x - y) dx dy 2. Sketch the region of integration…

A: double integral and changing the limit

Q: 6 cos3x cos4x dx

A: To evaluate: ∫π6π2 cos⁡3xcos⁡4xdx Let I = ∫π6π2 cos⁡3xcos⁡4xdx We know that 2cosAcosB =…

Q: The doubling time of an investment is the amount of time it takes to double in value. If an…

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Q: 0 Convert the following polar equations to Cartesian form and identify its graph. a.) r = 2 (3 cos +…

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Q: 5) Given the price-demand and price-supply equations below, determine the equilibrium price and find…

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Q: Find the equation of the tangent line to the function f(x) = 5* at x = 4. (Use symbolic notation and…

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Q: Differentiate the following using Chain Rule. 1. f(x) = (2x - 1)4

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: y' = X 2 h

A:

Q: x dv (2.v) - dx (V²1) dv (1+r) dx X 2 \-2 V-V²

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Q: 2 √₁² √√x² - 4x + 8

A: The solution is given in the next step.

Q: 1- Use the shell method to find the volume of the solids generated by revolving the shaded region…

A:

Q: In this question, you will solve an integral problem using the method of substitution. (a) Make the…

A: A detailed solution is given below

Q: A company has a security system that uses digits from 1 to 6. a) How many 3-digit security codes are…

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Q: 2) Given the vectors a-[4, 2, -6], b-[6, -3, 2], and c-[-5, 0, 4], simplify the following vector…

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Q: 5.) Find fog and go f, and their domains. f(x)=√x - 4, g(x) = x²

A: Given :f(x)=x-4g(x)=x2

Q: Consider the series. 2 3 4 10 (¹) + ( )² + ( )² + ( )* +-- ∞ This series can be written as a…

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Q: 6+ З +2 (2x+1)= 8

A: 6x3 + 2(2x+1) = 8 2x + 4x + 2 = 86x + 2 = 86x = 8 - 26x = 6x = 66 = 1

Q: 10. Find the limit using any technique. The limit of f(x) = 2x² - 3 as x approaches -3. 15 21 limit…

A: To find limit of f(x)

Q: M8 n=1 3 n 4 n* + 4

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Q: . Find the derivative of a composite function using the Chain Rule or General Power Rule. 1.)…

A: As per the company's guidelines, we are supposed to solve first three sub-parts for you, kindly…

Q: find d2y/dx2 at x=2 a. y=x^(2) (\sqrt(x)+2) b. y=3x^(2)-(4)/(\sqrt(x))

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Q: 2. a) Write sin(3-1) in the form of a + bi. b) Find all the values of (3)-in

A: Concept: Simplifying expressions: Expressions are mathematical statements with at least two terms…

Q: 0 Compute the integral: I alned

A: LetI=∫01xlnxdxApply integration by…

Q: lim X→+∞ 5 In³ x 2 X²

A: Let's evaluate limit.

Q: The general solution of the D.E. dy/dx + y cotx = 1 is a. y -cotx + c sin x b. y = -tanx + C CSC X…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Find the general equation of the circle of curvature of the parametric equation t+1 X: ; y = ±…

A: This is a problem of finding equation of the circle of curvature. Based on the general formula and…

Q: 6) Calculate - dx for z = ln(x + y²).

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Q: 1- Use the shell method to find the volume of the solids generated by revolving the shaded region…

A: