a graph of f(x) showing all si f(x) = : (Q.infinity) symptote

Q: a) By using the graph of function y = cos x, graph the function y =- cos (3x +) x-8

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

Q: The limit below represents the derivative of some function f(x) at some number a. 10 sin(2 + h) – 10…

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Q: The following limit represents the derivative of a function, f, at some number a: lim h->0  sin(16π…

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Q: e-(1+x)+/x Evaluate lim tanr

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Q: 1- cos x The lim X40 sin x is equal to O 2 Zero O-

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Q: et +e-& – 2 Evaluate L = lim Hint: use L'Hospital's Rule. 1- cos x |

A: Use L hospital rule

Q: 2. f(x) = sin(x) lim sin(x) - et x + 00

A: Calculate the limit and horizontal asymptote in the following way: (2).              f(x) = e-xsinx…

Q: Find the value a > 0 such that the tangent line to the graph of f(x) = x²e-2x at x = a passes…

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Q: 1 5 arctan x/ = ? Use L'Hospital's Rule 4 lim 4 arctan-

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Q: lim (x)-(.0) tan , -= (A) Does not exist (B) e? (C) 0 (D) ezn (E) e *IN

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Q: lim a-1 In(1-x) dx X

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Q: e* +e* -x? -2 1) Lim sin² x – x²

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Q: QI// Let f(x) = (1+sin?x) then Limit of f(x) as x approached to zero equal to:

A: Given f(x) = 1+sin2xx2

Q: 27. lim (x + cos

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Q: e lim tan(x).

A: The given limits,limx→π2-tan(x)limx→π2+tan(x)

Q: sin (-) if x + 0 g(x) = if x = 0. Is g differentiable at 0? If so, find g'(0). Justify your answer…

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Q: x arcsin(kx) lim sin((k – 1)x)(e2- – 1) ||

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Q: i) lim e5x cos x 个。 ン

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

Q: 1. How do I solve this?     2. How would I find the tangent line to the graph at x=-1

A: Consider the given function.

Q: Let cos x if x 0 (a) Sketch the graph of f (x). (b) Is f (x) continuous at x = 0? Give reason(s)…

A: Explanation of the answer is as follows

Q: 3-f(x) = tanh¯1(cos(e*))

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Q: Let k(x) = tan−1 x. Find the value of k(9)(0), the 9th derivative of tan−1(x) at x = 0.

A: Given

Q: lim x goes to pi/2 at cot x

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Q: e) lim 1-cost sin²)

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Q: The following limit is the derivative of a composite function g at some point x = a. sin(x/2 + h) -…

A: We have to find the composite function g(x) at some point x = a using the given limit. Also, find…

Q: 1) Find the derivative of the function. Simplify if possible. ? = sin ? cot ?

A: 1) We have to find derivative of y=sinxcotx It can simplify it as: y=sinx·cosxsinxy=cosx…

Q: The derivative of a function f is given by f'(x) = esin z On what intervals is f decreasing? cos x –…

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Q: c Functions. Prove the identity cosh x – sinh x = e x-

A: We have to show the given condition

Q: 1. Let f(x) = Find the equation of the tangent line to the graph of f'(x) at the point x² + 1 where…

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Q: Question1. Find the derivative w.r.t x. f(x) = Cos²(3Vx) f (x) = x3 – x. Also draw the graph of f…

A: Solution:To find the derivative with respect to xFormula:dydx=dydududxddx(cos x)=-sin…

Q: B. Use the definition of the derivative (the limit of a difference quotient} to find a formula in x…

A: Given function : Using the definition of the derivative formula:

Q: The equation of a tangent line at a point (x₁, f (x₁)) where limh→0 f(x₁+h)-f(x₁) h = +∞ is x = x1.…

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Q: The function f is defined by f (x) = x² + 3 cos (x² – 3). The graph of f crosses the x-axis at one…

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Q: The following limit is the derivative of a composite function g at some point x = a. cos(t /6 +h) -…

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Q: The graph shown represents the graph of THE DERIVATIVE ƒ' (x) of an unknown continuous function…

A: Given, Graph of the f'(x) is shown as:

Q: 57. Extension of Example 8 Show that cos (x) is dx sin (x). 180

A: The objective is to show that ddxcosx° is -π180sinx°. The function cosx° is given in degrees bu the…

Q: Please show step-by-step solutions.

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Q: lim e* cos X

A: From the given data:

Q: ind derivative w.r.t.x: f(x)=x3 -x. Al

A: Given,         f(x)=x3-x

Q: e* – 1 lim x-0 tan 2x

A: Given: limx→0ex-1tan2x

Q: sin x 3) lim

A: Explanation: Find the limit limx→0sinxx3

Q: The derivative of a function f is given by f'(x) = esin for 0 < x < 9. On what intervals is f…

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Q: Solve for the derivative of the given functions using the Chain Rule formula.Let g(x) = sin (cos…

A: Since, g(x)=sin (cos x)g'(x)=cos (cos x)ddxcos (x)⇒g'(x)=cos (cos x)(-sin (x))ddx(x)⇒g'(x)=-cos (cos…

Q: e function g is defined for x > 0 with = 2, gʻ(x) = sin (x + ), g"(x) = (1-) cos (x +) e line…

A: In this question, concept of tangent is applied. Tangent A tangent is a straight line or plane that…

Q: The limit below represents a derivative f' (a). Find f(x) and a. sin ( +h) – 1 lim h-0 h f(x) = a =

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Q: Prove the identity.  cosh x - sinh x = e -x

A: Consider the given identity of L.H.S as coshx-sinhx

Q: e* + e-x – x² –- 2 lim sin? x – x2 х — x→0

A: To evaluate: The limit limx→0ex+e-x-x2-2sin2x-x2. Calculation: Use L'Hospital rule to evaluate the…

Q: (c) Graph f(x) = sinx, 0≤x≤ 2π and also graph f-¹(x).

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Q: lim as x--> +infinity of (ln(2x))/(pi^x)

A: Using L hospital rule then find tha limit