a) Use the Product Rule to find the derivative of the given function. b) Find the derivative by multiplying the expressions first. y=(5-√√x+6)x²

Q: Find the general solution of the differential equation: y'+3y = 4 sin(3t) Use lower case c for the…

A: A detailed solution is given below.

Q: In each of Problems 9 through 16: a. Find the solution of the given initial value problem in…

A: Given that a initial problem and we find its solution and plot the graph of this problem solution.…

Q: Point      Line (-8, 7)      x + y = 13 (a) Write the slope-intercept form of the equation of the…

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Q: 98 x = 62° 29° NOTE: The triangle is NOT drawn to scale. Answer the following: Round your answer to…

A: We are required to find the value of x

Q: g) f(x)=√1-ecos(1-x²)

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Q: Use the shell method to find the volume of the solid generated by revolving the plane region about…

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Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: Match each function (a, b, c, d) with its derivative and explain how you knew. Not all derivatives…

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Q: (b) Find the limits as x approaches 4 from the left and from the right. lim f(x) = X-47 lim f(x) =…

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Q: 1. Find the volume of the solid generated by revolving the region bounded by the given lines and…

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Q: Suppose that 9x² +9x+7 < g(x) < 7x² − 8 x+7 for all x 0. Compute the exact value of lim g(x) x→0

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Q: Assume that the function G(x) is measured in zots and x is measured in toots. What units would G'(x)…

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Q: more than one option is the answer.

A: fx=x2-x-20x-5,x≠510,x=5 Also, we have computed that, limx→5fx=9 Let's verify each option one by one.

Q: Solve the exact equation ( 1⁄2 + 2x) dx + ( + + 2y) dy = 0. x Y The solutions are of the form F(x,…

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Q: Pittsburgh, PA and Miami, FL lie approximately on the same meridian. Pittsburgh, PA has a latitude…

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Q: Please show examples and final answers

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Q: Using the sine and/or cosine law, sin A a c² = = sin B b a² + b² 2ab cos C Find the magnitude of the…

A: Given query is to find the resultant of the vectors.

Q: Solve the exact differential equation (-5 sin(x) - y sin(x) + 4 cos(x)) dx + (cos(x))dy = 0 where…

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Q: Sketch the graph of a function f that satisfies all of the given conditions. lim f(x) = 1, lim f(x)…

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Q: Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f…

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Q: Suppose the demand for a certain item is given by D(p)=-5p²-6p+800, where p represents the price of…

A: Given demand function D( p ) = -5p2 - 6p + 800 where p = price of the item in dollars

Q: 2.10

A: (a)  x=3y-3y3 ,  about x axis volume(V)=∫ab2πR(y)H(y)dywhere R(y) is radius H(y) is height

Q: Solve the oblique triangle. Clearly show supporting steps and diagrams. Round to the nearest tenth…

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Q: Solve the following differential equation u'(t)+u(t) = sin^2(t)u'(t)+1 with the initial condition:…

A: We are required to solve the differential equationu'(t)+u(t)=sin2t.u'(t)+1 given uπ4=5

Q: Find f, fy, f₂. f(x,y,z) = (4x² + 4y² + z²) e

A: As per our guidelines we are allowed to answer only one question. Kindly repost the other question…

Q: Consider the function f(x, y) = 2x³ + y on the region {(x, y) | x² + y² ≤ 16}. Find the absolute…

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Q: 1 (t² +3t+1)/2 19½/2 f) f(x) = -

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Q: Use the graph of G shown to the right to find the limit. When necessary, state that the limit does…

A: We want ot find limx→3G( x ) = ?

Q: 9x-7 2x²-3x+1

A: Topic - Partial fraction decomposition We are given 9x-72x2-3x+1

Q: Find parametric equations for the line. (Use the parameter t.) the line through (-8, 2, 7) and…

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Q: Find a value c in [1, 4] such that f(c) is equal to the average value of f(x) = e2x + 1 on [1, 4].…

A: f(x)=x2x+1  on 1,4formula for average value  is favg=1b-a∫abf(x)dx∫exdx=ex

Q: (LT3.a) Use the Fundamental Theorem of Calculus to find the exact value of the definite integral √2…

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Q: The curvature of the helix r(t) = (a cos t) i + (a sin t)j + bt k (a,b20) is k=- 2,2 a+b What is the…

A: Given helix:- rt=acostiasintj+btk

Q: Find an equation of the plane. the plane through the points  (4, 1, 4),   (5, −8, 6),  and  (−4, −5,…

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Q: P(1, 0, 1), Q(-2, 1, 3), R(6, 2, 5) (a) Find a nonzero vector orthogonal to the plane through the…

A: Given;  P(1,0,1), Q(-2,1,3), R(6,2,5).

Q: Find the derivative of the following function by first expanding the expression. f(x) = (2x + 7)…

A: INTRODUCTION To calculate the derivative of a function, one must use differential calculus. This…

Q: Find parametric equations for the line. (Use the parameter t.) the line through the points (-5, 2,…

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Q: Find the cosine of the angle between the normal vectors to the planes x+y+ 2z = 3 and 2x -y + 2z = 5

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Q: Find all points (x,y) on the graph of f(x) = 2x² - 5x with tangent lines parallel to the line…

A: Given: f(x)=2x2-5x with tangent line parallel to line y=7x+2

Q: ○a=3 O 10. Select the value of such that alog(x) is equivalent to log₂ (x). a=9 a = 1 3 Oa= √3

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Q: Consider the following points. (X₁Y₁)= (-5, 7) (x₂1 y ₂) =(4,-5) (a) Find the distance between the…

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Q: Let f(x) = x*|x| Find a formula for f'

A: Given f( x ) = x| x | As we know that ddx| x | = x| x |

Q: ius, r, in centimeters, of a melting snowball is given by r = 60 - 2.5t, where t is the time in…

A: Given query is to find the volume formula in terms of time.

Q: the equation. 29. y' - 2y = 1²e²t

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Q: How do we know that eª and In x are inverses of each other?

A: The given two functions are ex and lnx We have to prove ex and lnx are inverse of each other .

Q: Which of these does it makes sense to model with a continuous function as a function of time? Write…

A: oxygen concentration in a patient's blood: Continuous heart rate on the scale of seconds:…

Q: 60° 14 The hypotenuse of a right triangle with base angle 60° and base 14 is

A: GivenIn the right triangleBase=14Base angle is 60°   We are required To find the hypotenuse

Q: 2x³6 Solve differential equation. You may leave your answer in implicit form. dy dy + +y =…

A: If M and N are functions of x and y and ∂M∂y=∂N∂xsolution is given by∫keep y constantMdx + ∫term…

Q: Suppose the speed of a car approaching a stop sign is given by v(t) = (t-20)², for 0 st≤ 20, where t…

A: Please see the below picture for detailed solution.

Q: Pls help with these

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