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Q: Suppose f'(x) = sin(2x²). d ; f(7æ) =| dr d de f(32®) = [

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Q: Direction: Solve the following equations using separation of variables. 3. 2xy + 6x(x² – 4)y' = 0…

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Q: Evaluate by separation of variables. dß %3D и(1 — и?) sec? р du 2 tan B+ sin 2ß = C – (1 – u?)? 2u?…

A: To solve the given differential equation.

Q: dy = 8x - 7 and y(9) = 0. dx Find the function y(x) satisfying

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Q: Evaluate the integral where D is the region bounded by y = x, y = 2, and r = 0. Hint: One order is…

A: We will solve this question by changing the order of Integration.

Q: V-2 Evaluate lim X8x2-7x-8 O 2/7 O None of these O 1/9 1 O 1/12

A: We have to find limit

Q: Question Use the First Derivative Test to find the location of all local extrema for the function…

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Q: The length and breadth of the floor of a room are 30 feet and 20 feet, respectively. Square tiles of…

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Q: A mass that weighs 8 lb stretches a spring 48 in. The system is acted on by an external force of 8…

A: Given

Q: For what values of x is the graph of y=xe-4x concave down

A: Given  that y=xe-4xSolution :if d2ydx2<0 then concave down.

Q: What is tan 0 if sin 0 = cos 0? -1 1 O Option 1 O Option 2 4 O Option 3 O Option 4

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Q: [csc2e cot 6i – 5 cot 6 de

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Q: y^2= (x^2 + 2x)/ x-1 find the x and y intercept, symmetry, region/scope, asymptotes, critical…

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Q: AVERAGE VALUE OF A FUNCTION QUESTIONS A. 3x2+4x-7, [-2, 5]

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the general solution for the following equation: y''' + 3y'' – 4y' – 12y = 0

A: Solve the differential equation by assuming eλx for some constant λ.

Q: Let f be a continuous function on [a, b]. Which of the following statements is false A If k is a…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Select from multiple choice and fill in the blanks

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Q: If the surface area of a cube is increased by 96%, by how much has the edge increased? 96% 92% O 40%…

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Q: -Ihd the x-values of all points where the function has any relative extrema. Find the value(s) of…

A: f(x)=-103x3-512x2-5x+19f'(x)=-3×103x2-51×22x-5⇒f'(x)=-10x2-51x-5f'(x)=0⇒10x2+51x+5=0By quadratic…

Q: The barrel of a fountain-pen cylindrical in shape is 7 cm long and 5 mm in diameter. A full barrel…

A: Given that the fountain pen barrel is cylindrical in shape.

Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 1. y sinx – xy² = c -

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Q: 6.(Somewhat tricky) Use an appropriate substitution to solve: (a) dy y + x dx (b) (y³ + y?x) dx – x³…

A: To solve the following differential equation

Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A: use the definition  of exact or non exact.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find dy and simplify whenever possible. dx secx+tan x 1. у %3 sec x-tan x - 2. y = e-* cos e¯* – sin…

A: 1. y=secx+tanxsecx-tanx2. y=e-x cose-x-sine-x3. y=arctanx-1+x2

Q: Substitution Method dy xy = 0 (7) (x² – y²) (8) 2xy = x² + 2y² - - dx dx (9) (1 1 3r sin v)dr r2 cos…

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Q: 2t2 + 38 sinh 16t

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Q: Fove that y = ln|| is a solution to 1+e-22 - xey-x² . Use the initial values x = 0 and y = 0.

A: Given query is to find the solution of the differential equation.

Q: On which interval is the function increasing? * 40- 20- 2. 20- -40- O (- 3, 3) O (3, 5) (- 5, - 3) O…

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Q: Which of the following trigonometric expressions is NOT equivalent to 1? * csc? 0 – cot² 0 cos? 0 +…

A: To determine which of the given trigonometric expressions are not equal to one.

Q: s the volume of the frustum of a cone whose upper base is 16 cm in er, lower base 10 cmin diameter,…

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Q: Which of the following is not equivalent to sin 0?

A: We are asked to find which is not equivalent to sinθ

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: We need to find minimum distance.

Q: 1+cos4x 1. 1-cos4x -csc2xdx

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Q: Integrating Factor by Inspection: (1) y(x² + y² – 1)dx + x(x² + y² + 1)dy = 0

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Q: x² – 16 Evaluate lim x4 2- Vx O -32 None of these 1 O 32 O does not exist

A: Given  Lt   x²-16/(2- √x)        x->4

Q: 7y" - 18y %D

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Q: s e8*(x³ + x²)sec² (x*e3* + 1) dx

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Q: Write the equation of the tangent line to the graph exy + cos v = + COS at He %3D point (-0.3, 2.12)

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Q: Evaluate xe*dx. -3

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Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

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Q: From a window 30 feet above the street, the angle of depression of the curb on the near side of the…

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Q: Suppose that enrolment in CLSU has been increasing over the years since year 2014 according to the…

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Q: S e2x sin 2xdx

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Q: (w°t wz? -z) dw +(z² tw² -w) dz= 0

A: Let's find.

Q: estion Evaluate:S sin (3x) cos³(3x) dx r answer estion Ising Trigonometric Substitution, evaluate: -…

A: Solution:

Q: What is the magnitude of the vector cos 0 i + sin 0j+ 1? 01 O2

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Q: dx V3+2x-x2 10.

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y =…

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