y=-sinx . 3π X 2 元 2. 2 N/2

Q: Find an interval of definition for the equation x^2 dx/dt = 3x^3 t^2

A: Domain of definition is where X(t) is defined

Q: 8) Find all values of t for which x = +5, y = t lnt – t has a vertical tangent line

A:

Q: d dx A.sinh(Inx) B.–sinh(Inx) sinh(Inx) C.- X -cosh(x) D. X cosh (Inx) =

A:

Q: 9 tan t Find the derivative of the function y = 2 + 2 sect dy dt

A: Explanation and solutions is given below....

Q: What is the closest value to the instantaneous rate of change of the following function at x = T?…

A: Ans:  Given  fx=2 cosx-π2  at  x=π          ⇒fx=2cosx coπ2+ sinπ2         ⇒fx=2cosx 0+sinx1…

Q: cosh x dy + (sinh x)y = e-* dx

A:

Q: 0 to x = 5 Determine the average rate of change of the function y = sinx from x =

A:

Q: 7) Find the instantaneous rate of change of f(x) = ecos(z") + sin(In(8²)) at x = 1.

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Q: -2x²+2x+1 Find the equation of the tangent line to the graph of F(x) ev dy at x = 0. sech z

A:

Q: Let y = x sin(2x). (a) How fast is y changing at x = t? (b) Find an equation of the tangent line to…

A: Given y=x sin(2x)

Q: Calculate the average rate of change of each of the following functions over the interval…

A:

Q: x sin(2x). (a) How fast is y changing at x = n? Let y = (b) Find an equation of the tangent line to…

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Q: Find the rate of change of the distance between the origin and a moving point on the graph of the…

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Q: Two students are calculating the instantaneous rate of change of y= sin(x) at x = Student A claims…

A:

Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: d'y Find the second derivative, dz? where y is related to z implicitly by the equation below. 2² –…

A:

Q: Q3) Find the derivative of y for all functions the following (1) y = 0 (sin (In 0) + cos (In 0)),…

A: Since you have posted multiple questions, we have solved the first question for you, if any specific…

Q: A particle moving along the x-axis has velocity function v(t) = t sin t. How far does the particle…

A:

Q: Find G(1), G'(0), and G'(π/4), where G(x) =

A: Here we have;  G(x)=∫1xtant dt

Q: The slope of the line normal to the graph y = 2 ln(sec x) at x = is: O-1/2 O non-existent O-2 2

A: The graph y=2lnsecx at x=π4

Q: Can you help me with this problem step by step?

A: Given that

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A:

Q: dy Find the derivative of the function In 3y= y sin 3x + etz Answer.

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Q: True or False The velocity of a particle whose position at time t is s(t) is the derivative s′(t).

A: Our Aim is to tell whether the statement the velocity of a particle whoseposition at time t is s(t)…

Q: The height (in centimeters) at time t (in seconds) of a small mass oscillating at the end of a…

A: We find the velocity function by differentiating h(t) with respect to t

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A:

Q: /4 Find the derivative of y with respect to t. (a) y = In(3te-1) (b) y = esin t (In t² + 1) (c) y =…

A: Given functions,  (a)  y=ln3te-1 (b)  y=esintlnt2+1 (c)  y=tlog3e(sint)(ln3) The objective is to…

Q: (5) cosx (C)tanx . (D)sinx. (D) 10 5: The average rate of change of f(x) = x² + x on the interval…

A: According to rules, I need to solve only one question when multiple questions are posted So repost…

Q: Find the derivative of y=2ecos.x)(sin(5x)) d'y Calculate as a function of t if x=t-t and y=t-t 2 dx?…

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Q: What is the instantaneous rate of change for α=arctan(2-r/r) at r=0

A:

Q: The derivative of y=eov? +cosh/x equals Select one: O y' = 2/x et +sinhx + sinh/x O None O y'=@ov +…

A: This is a composite function. Therefore we have to use rules for derivative of composite functions.

Q: 7. Find dy and hence determine the rate of change of y with respect to x for the following…

A:

Q: dy da Find the derivative of the function x° In 3y = y sin 3x + e5 x %3D Answer:

A:

Q: 1) Find the Linearization x of the function -V1+2x when x is near 0 Find the equation of the tangent…

A: As per Bartleby guideline if more than one question is asked only first question to be answered…

Q: The derivative of the function y = sin VE at a = is equal to %3D 4 14

A:

Q: 1 secz The derivative of the function y at z = 1 is equal to Select one: O a.-1 b. Does not exist…

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Q: 3n Find an equation of the tangent line to y = 7 sin(x) at x = .

A:

Q: Find the average rate of change (AROC) of the following functions over the interval [60 ≤x≤180] y =…

A: using , average rate of change…

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A: Given a point is moving along the graph of the given function at the rate of dxdt. Given function is…

Q: Q2\A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Given that,

Q: (a) Find the slope of the line tangent to the curve y = sin x at the point where x = T/3. (b) Show…

A: (a) we have to  find the slope of the tangent line to the curve y=sin5x at the point where x=π3. as…

Q: cx+ln x Determine the equation of the tangent line to the graph of f(x) = [" = cosh (√2t - 1) dt at…

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Q: 10. Let y = In(x' + sin 3x). Find dy/dx.

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Q: The tangent line to the graph of y = f(x) at the point (8, 9) has the equation y = 2x – 7. %3D (a)…

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Q: 2. : Consider the function ry + cos y + x 2+ xy. (a) Find the derivative, dy/dx. (b) Find the…

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Q: Calculate the instantaneous rate of change of g at the point (4, 1, 2) in the direction of the vec…

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Q: What is the second derivative of the function y = -6 sin x cos x where x is? Round your answer to…

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Q: Consider the step size h = 0.1 and h = 0.001, how does the step size affect the accuracy in %3D…

A: Given that, A=82, B=16.4f(x)=Aex+Bx2sinxFor the given values of A and B,f(x)=82ex+16.4x2sinxWe need…

Q: Let -sin (y-4x) Find the rate of change of z with respect to y at the point (2, 1) with x held…

A:

Q: 1 - Find a formula for the rate of change dv/dt of the volume of a balloon being inflated such that…

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