We obtain the graph of the function below by shifting the graph of f(t) = sin 2t a distance of how many units and in what direction?* f(t) = sin(2t - T) 3.

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A: Let the given curve be y=fx.Given that dydx=x+223+1Also, it has an x-intercept of -2, that means,…

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A: Determine the derivative for f(x). fx=lnx5f'x=ddxlnx5=ddx5lnx5×ddxx5=1x5×5x4=5xSo, f'x=5x

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Q: 12. Given the point ( 2, 1) on a tangent line to the curve ƒ(x) = x² − 2x + 5 find the point(s)…

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Q: 5cos3(x) Гу 3 sin(3–2x) + tan? (3x? — 4х) — csc(/2x — 1

A: Differentiate y w.r.t x.

Q: 3. (a) What is the derivative of sin(g(z))7 (b) What is the derivative of sin(2r + T)?

A: We have to find

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Q: 3. Find the derivative of the function, and do your best to simplify the result. [P372]| arcsin 3r…

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Q: Q2: Find the tangent line when the function 1- y= 4+Cot x -2Sec x and point ,0)

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Q: 1. In the open interval (0, T/2) , find the point where the slope of the curve is 4? y = tan x

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A: A function is a relation which maps each value in its domain to exactly one value in its range.…

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Q: 30. Find the points on the curve y = tan x, -7/2 <x< T/2, where the tangent is parallel to the line…

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Q: a)find an equation for the tangent line drawn to the graph of f(x)=1/x at x=2. b)Find the exact…

A: a)

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Q: 40. For what value(s) of x does fAx) = (x - 4x – 5) have a horizontal tangent?

A: 40.) f(x) = (x² - 4x - 5)³  So, f'(x) = 3•(x² - 4x - 5)²•(2x - 4) So, f'(x) = 6•(x² - 4x - 5)²•(x -…

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Q: 21 Find the equation of the tangent i ne OF the graph of yEra y= xe at the point ( ). y=? -2X

A: The objective is to find the equation of the tangent line.

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Q: 1) tan 0 13 5.

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Q: If y = -cos x, what x-value corresponds to a y-value of between T and 27? ? ]T

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Q: Q3 Find the equation of the tangent line to the function f(r) =x+7 at r 1. Show your work.

A: f(x) =x3 +7 Let y = f(x) = x3 +7, we have to find the tangent at x=1 , so value of y at x=1 is  f(1)…

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Q: nd the equation of the tangent line to the curve when x has the given value. Find the equation of…

A: Our Aim is to find the equation of the tangent line to the curve x2+5xat x=4.

Q: d Using the definition of derivative, show that: (10 sin(x)) = 10 cos(x) explain your steps clearly.…

A: We have to show   d dx10sin(x) =10cos(x) By definition of the derivative we know…

Q: 12. Given the point ( 2, 1) on a tangent line to the curve f(x) = x² – 2x + 5 find the point(s)…

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A: topic - double derivative of a function

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Q: (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an equation of the tangent line to the…

A: Consider the given function as y=5x1+x2

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.