s (t) = 1+ sin t 1 + cos t

Q: Q5.1 A particle of constant mass m moves along the x-axis. Its velocity v and position a satisfy the…

A: Given :12mv2-v02=12kx02-x2k, v0, x0 are constant

Q: Find the derivative of the function f by using the rules of differentiation. f(x) = (1 + 2x²)² + 3x³

A: We need to find the derivative of  fx=1+2x22+3x3

Q: If 3x - 4 ≤ f(x) ≤ x² − 3x + 5 for x ≥ 0, find lim f(x). - X-3

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Q: nd dy for d²y dx² y(x) = cot(x)

A: Given query is to find indicated derivative.

Q: etermine whether or not F is a conservative vector field. If it is, find a function f such that F =…

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Q: Find the area of the surface generated by revolving the curve y = - 18' -2√2 ≤x≤0, about the x-axis.

A:

Q: Suppose that the area, A, and the radius, r, of a circle are changing with respect to time and…

A: given  A=πr2given  drdt=2 cmswhen r=5 cm drndr=nrn-1

Q: 3. Suppose f(3) = 2 and f'(3) tangent to g(x) at x = 1. = 8. Let g(x) = r² f(3x). Find the equation…

A: Topic = Application of derivative

Q: Find (d/dx) (2x(3/2)−5x(1/4)+4)

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Q: The functions f and g are defined as f(x) = 8x + 5 and g(x) = 10 – 9x. b) (f+g)(x) = (Simplify your…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: Solve for difference quotient, and explain why you are doing each step. As if you are teaching this…

A: Question -   Solve for difference quotient,   F(x)=1/(5x-8)

Q: (c) the equation of the tangent line at the point (4, 3).

A: We will find the required.

Q: 3. Given two vectors x = [0, 1, 1] and y = [- 3, 0, 0], use your knowledge of vectors to determine…

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Q: Let a be a real number. Which of the following statements about the infinite series Σ A B C D The…

A: Please see the below picture for detailed solution.

Q: Given f(x) = x³ + 2x²-x-2 √x-1 lim f(x). x→0 lim f(x). 2+1 solve for the following limits:

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Q: Find the values of x₁ and x2 where the following two constraints intersect. (Round your answers to 3…

A: Given Inequlities,10x1 + 5x2 ≥ 50,1x1 + 2x2 ≥12

Q: #4

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 9) Given f(x)=x²-2 a) Find an expression for f¹ (f's inverse) b) Graph both f(x) and f¹(x) on the…

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Q: ax Assume that x = x(t) and y = y(t). Let y = x³ + 6 and dt Find dt dt = when x = 1. (Simplify your…

A: We know the Power rule: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x Use the common derivatives:…

Q: 1 please

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Q: Perform the indicated operations and simplify your answers. i. -(60-301)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the value of b and e of the piecewise function f(x) = (bx² + 3 lc - 2x ,x≤2 , x>2 Where; lim…

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Q: Answer as directed. Show complete and neat solution. 1. Using the definition of derivative, find the…

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Q: 3. Find the Critical Point(s) (both coordinates) of the function y = x².Inx.

A: The given function y=x2 lnx. We have to find the critical points of the function.

Q: 10. f(x)=x²+6x+5 a. Find the vertex using the vertex formula. b. Find the intercept(s). c. State…

A: Given equation:- fx=x2+6x+5

Q: (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) π 3π 2'…

A: The given function is: fx=9 cos2x-18 sinx,  0≤x≤2π

Q: Prove that the following function is harmonic and find its harmonic conjugate: 2e^x cos y

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Q: lim f(x) lim 8118 lim f(x) x → 1 lim_f(x) X-3 f(x) the equations of the asymptotes (Enter your…

A: We have given graph of the function  From given graph  limx→∞fx=-2 limx→-∞fx=2 limx→1fx = Does Not…

Q: The marginal cost function has the special interpretation as an approximation to the exact cost of…

A:

Q: Find dy/dx by implicit differentiation. 5x² - 3y² = 4 dy/dx =

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Q: Sand falls from a conveyor belt at a rate of 14 m³/min onto the top of a conical pile. The height of…

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Q: If No - My M equation = Q, where is a function of y only, then the differential has an integrating…

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Q: The general form of a parabola is y^(2)-4x+4y-8=0. What is the standard form of this parabola?

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. tan(2x…

A: Given data : Find dy/dx by implicit differentiation. Then find the slope of the graph at the given…

Q: An individual has $45,000 to invest: $32,000 will be put into a low-risk mutual fund averaging 6.1%…

A:

Q: The general solution of (D4 -2D³ -5D² +6D)y=0is -3.x a. y=C₁e* +C₂e-³x + С₂е²x + C₂ 3.x -2.x c.…

A: Given : D4-2D3-5D2+6Dy=0

Q: Find lim as x appraoches to infinity of (2x√ (x^2+x+1) / (x^4 - 9)

A:

Q: Find the linear approximation to the function f(x, y) = e* cos y at (x, y) = (0, π) A. L(x,y) =…

A: Given: f(x,y)=excosy at (x,y)=(0,π)

Q: 2 5 4 -5 Let A = 4- [3 ] and B = [] -3 - 1 3 k, if any, will make AB = BA? What value(s) of

A:

Q: 2. Suppose that {an}1 converges to 1 and {bn}1 converges to 2. For n € N, define an: if n is odd; Cu…

A: Please see the below picture for detailed solution.

Q: K Use the given graph to find each of the following: a) the zero of the function b) the x-intercept…

A: Given query is to find zero of the function and x intercept.

Q: Find the volume of the solid that results when the region bounded by x=y^2 and x=2y+15 and is…

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Q: What is the solution to a differential equation 2(y+e')+x(1+e³)y'=0? b. x(y² +e") = C d. x² (y…

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Q: lim x→∞0 2x√√√x²+x+1 x4-9

A: Explanation of the answer is as follows

Q: Differentiate the function G(x)=√ +2e² =) =

A: Given query is to find derivative.

Q: The populations (in thousands) of two different cities are given by P1=45(1.038)t and P1=48(1.025)t,…

A:

Q: 2. Find the difference quotient of f(x) = x³ -1. Simplify until h in denominator cancels out.

A: f(x)=x3-1difference quotient=f(x+h)-f(x)h(a+b)3=a3+b3+3a2b+3ab2

Q: Let M = xey−(z^2), x = 2uv, y = u − v, z = u + v, compute (∂M/∂u), (∂2M/∂2u), (∂M/∂v), (∂2M/∂2v)…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: 26. (a) Find an equation of the plane that passes through the points A(2, 1, 1), B(-1,-1, 10), and…

A: (26) According to our guidelines , we can answer only first three sub-parts. Kindly re-post other…