nt) Find the value of the constant c that makes the following function continuous on (-co, 00). {: + 1 if a E (-o, 4] =D{ ca² -1 if a E (4, 0) ca -1 if a E (4, c0) C =

Q: Find the interval on which the curve 1 dt 3+t+3t2 y = 1 is concave upward. Note: When using interval…

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Q: O Find the values of a and b to make the function ffx) is continuous everywhere sin ax if x < 0 f(x)…

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Q: Determine the maximum and minimum values of the function f(x)= ex cos²x on the interval x= [0,2π].

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Q: A function f is defined by f (1x) = / Cos(x –1) dt Cos(t) f (x) = Simplify f(x) and evaluate f ()f…

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Q: What is the maximum value of y = cos x. For -5 < x <? 1 2 O 1/2

A: Topic = Derivative

Q: Does the function f(x) = 5x − cos(x) + 4 have a root on [−π, 0]? Justify your answer.

A: Explained below

Q: Calculate the approximation for the given function and interval.

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Q: 4. Suppose fand f'are differentiable functions of x. Given f' (4) = 0, f" (-), and g(x) = (). log…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

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Q: 1. Determine the absolute extrema of f(x) = (cos x − 1) sinx on [0, π], if they exist, and identify…

A: As per our policy, we are allowed to attempt only first question. Kindly post remaining question…

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Q: Find the intervals on which f is increasing and the intervals on which it is decreasing f(x) = - 2…

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Q: Find the intervals on which f is increasing and decreasing. f(y) = sin y - y cos y on 2' 2

A: Find your answer below

Q: Find exact Values for x in the interval 0,36O°) that satisfY the equation. 3Sin 2x+25inx=1+3cosx

A: We know that the formula of sin(2x) = 2 sin(x)cos(x).

Q: For f(x): cos(x) + 2, choose all values of c in the interval TT 37 guaranteed by Rolle's Theorem. 2'…

A: Given, fx=cosx+2 f'x=-sinx By Rolle's theorem, fx=cosx+2 is defined in the interval -π2,3π2, such…

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Q: b) Locate and identify the absolute extreme values of (i) In(cos x ) on[-"/4, "/3] (ii) cos (In x)…

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

Q: 2 V9 - f(x) = for -3 <x <0 TTX -x +3 coS for 0 < x < 4

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Q: 지2 2. If f is continuous and Sf(x) =. =6, evaluate (f(2sin@) Cos O d

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Q: For the function f (x) = cos² x – 2 sin x, find the interval(s) on which f (x) is…

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Q: If the function = (x)S x' +1 cos( 2 7x - a) if x < -1 is continuous at if x 2 - 1 x = -1 , find the…

A: Given: fx=cos2πx-aifx&lt;-1……1x3+1ifx≥-1……2   To find: Value of a where fx is continuous at x=-1.

Q: Find a point e satisfying the conclusion of the MVT for the function y(x) = 2e* on the interval [0,…

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Q: Find the open intervals on which the function is increasing or decreasing.

A: Given: y=x-2cosx Differentiate the function. dydx=ddx(x-2cosx)=1+2sinx

Q: Q1 (a) Sketch the graph of two continuous function g(x) = cos x and h(x) = on the same plane,…

A: Solution is here

Q: 19. Find the points of inflection on the graph of f(x) = x+2 cosx on the interval [0, 27].

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Q: What is the average of f(x)=2 cos (x) + 2 e between x=-3 and x=2 12- 10- -3 -1 00 8 6 2- 0 T 1 X 2

A: Q

Q: For f(x)=-cos(x)-1, choose all values of c in the interval (pi/2,5pi/2) guaranteed by Rolle's…

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Q: Find the intervals on which f(x) = cos2 x on [−π, π] is increasing and decreasing.

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Q: 9. Differentiate y = cos(x3/2 In x), do not simplify. x2-4 Using Calculus, show on which intervals…

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Q: 4. Determine if g is differentiable at x = 0 if 2 cos-1 x, if -1<x < 0 g(x) = %3D if x 2 0. x + cos…

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Q: 2. Find all values of 0 in the interval [0°, 360°) that have the given function value tan 0 = -V3.

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Q: Find the absolute extremum point(s) of f(x) = e1−cos x  on [−π/2, π), if any.

A: The given function is                                            f(x)=e1-cos x And we have to find…

Q: • Let f (x) = cos(x). Use central-difference formula of order 0(h²) with step size h 0.1 , 0.01 ,…

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Q: 3. (2') Let A+ cos x x 2. Given that q(x) is a continuous function, determine the value of A and B.

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Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = - 2…

A: Given, f(x) = 2cox - x              x ∈ [ 0 , 2π] f'(x) = 2 (-sinx) - 1 = -2sinx -1…

Q: 25. Find the constant(s) c for which the function f(x) is continuous on (-∞,+ ∞) (c? — х2 , х<2 12…

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Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(n/4) = 9?

A: f (x) = cx + ln ( cosx)To Find: For what values of c is f' (π4) = 9Proof: We will differentiate f(x)…

Q: Given f(x) = |x| for x € [-n,1]| Show that cos(2n – 1)x |x| 2 \xl = -- - (2n – 1)2 n=1 2.

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Q: 9 The function f is defined by f(x) = 2-3 cosx for 0 <x< 2n. %3D va lues (i) State therange of f

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Q: 10. Find all the values of a in the interval [0, 27] such that f (a,=) - fxx (a,=) = 0 for f(x,y) =…

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Q: Find the values of a and b such that the following function a² cos(x − 2) — 26(³-x), if x 2, is…

A: Topic = Limits

Q: Find f if f^ prime prime (x)=sin x+cos x,f^ prime (0)=4 , and f(0) = 3

A: The differential equation is given by f''x = sinx+cosx                ........1 The initial…

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Q: Determine the extreme values of the function f(x) = 2 cos(x) –1 on the interval [0, 27].

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Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(" = 5? 4

A: Differentiate the given function w.r.t. x.…

Q: Determine if g is differentiable at a = 0 if 2 cos-1 if – 1 0. x + cos x

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Q: given the function f(x)=(ax+b)cosx, where the function is increasing at x=pie/2

A: We need to check if the function is increasing at x.

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is  f '(π/4) = 9?

A: Consider the given function, fx=cx+lncosx first differentiate the function using chain rule as…

Q: find f (a ) if you Kinow that f'cz) = (1+tanz)sec"x 3 2. and that f(o) = 54.

A: dtan xdx=sec2x ∫ax+bn dx = 1a.ax+bn+1n+1+C

Q: (c) Use only the e – 8 definition of continuous functions to directly prove f(x) = x² sin(x) is…

A: In the given question we have to solve the part c of the given question. In this part we have to…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.