Continuous extension Find a value of c that makes the function 9x - 3 sin 3x 5x x + 0 f(x) = x = 0 continuous at x = 0. Explain why your value of c works.

Q: Determine the following limits analytically.

A: Given that : The limits is limh→0 sin(x+h) - sin xh , where x is a constant .       i

Q: Find the limits

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Q: Consider the function f(x)=4 sin x+x2+5x –10 with domain the closed interval [0, 27]. (a) Show that…

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Q: .f (x) = cos(-x) .f(x) = sin(8x) .f (x) = 2 sin(-5x) a) f'(x) = 2 sec(2x – 1) tan(2x – 1) %3D - b)…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: Consider the function on the interval (0, 27). f(x) = x - 2 sin x (a) Find the open intervals on…

A: Given problem is :

Q: | sin x| | sin x| а. lim b. lim x→0 sin x x→0+ sin x

A: Here we will find the given limits,

Q: sinh (x) esin h-' (x) sin h- (x) Vx²+1 -esin h¯' (x) sin h Vx²–1

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Q: Tangent line of a graph of f(x)=x(b^x)at x=1 is equal to the tangent line for the graph of…

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Q: sin -x/3) dx xp. Evaluate the integral| 19-x sin(x/3)dx -1 dp, %3D X-6/ 9-X

A: We have to find integral

Q: lim x→0 (sin3x sin5x/x2)

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Q: sin x – x cos x lim x→0 x – sin x

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Q: (0, f(x) = 7 sin2(x) + 7 sin(x) (a) Find the open interval(s) on which the function is increasing or…

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Q: How to avoid loss significant figures : (i) 1- cos(x), x is near 0. (ii) (v1+x² (ii) x - sin(x), x…

A: (i) Let,  f(x)=1-cos(x), x is near 0.  To avoid loss of significant figures,We can replace cos(x) by…

Q: Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 2   (a) Find the open…

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Q: (cos(2x) – sin(2x)cos(2x)) cos(x) – sin(x) For -dx=-F(x) + C. What is F (x)? 3 A (csc(x) – sec(x))3…

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Q: lim 2 sin(-2 x) 0.3) 4 sin (5 x)

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Q: An unknown constant Determine the value of the constant a for which the function x + 3x + 2 ifx + -1…

A: Given: f(x)=x2+3x+2x+1if x≠-1          aif x=-1 To determine: Value of the constant a for which the…

Q: Using Secant Method find the 3rd iteration of the function f(x) = sin(x) + x^2 + e^x. using interval…

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Q: (sin x + cos x) sin'x- cosx sin'x- cos'x cos-r COS X (sin x – cos x)2

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Q: lim sin (–3 x z) = z-3

A: To find- the limit.

Q: Using Secant Method find the root of f(x) = sin(x) + x^2 + e^x. using interval of [2 4] USE THREE…

A: This function does not have any root in interval [2,4]. Infact the function does notbhave any root…

Q: QI Find f' () for csc(x) cot(x) sec(x)' tan(x) f(x) = -(*) (4/3+8 -(*) 5/3+11 3/3 3/3 O 1A V3+1 -…

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Q: sin(3 – x) lim x→1 x2 – 5x + 6

A: Explained below

Q: Using identities Use the identity sin 2x = 2 sin x cos x to findd/dx(sin 2x). Then use the identity…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: cos2x – sin2x cos2x For dr3-F(x) +C. What is F(x)? cosr - sinr 3 2 cos'x+ cosx + A sinx + -sin'x B…

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Q: cos2x – sin2x cos2x For -dr =-F(x)+ C• What is F(x)? cosx - sinx A sinx – cosx) - B 2 sinx + -cos'x+…

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Q: sin(x ²–4) -4) lim x+2) tan (x+2) x→-2

A: Rearrange the expression than Apply the limit and simplify.

Q: f(x) = x sin x

A: Given data:     The given function is: f(x)=x sinx. STEP-1 The expression for the limit of the…

Q: () lim x→0 .2 x cos

A: We have to find the limit: limx→0x2cos1x After putting limit value, limx→0x2cos1x=0×cos10 Since 10…

Q: Absolute maximum and minimum values of f(x)= 2cos(x)+ sin(2x) on the interval [0, pi/2]

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Q: Finding the extrema of f(x) = 2x² – 3 x³ on the interval [0, 1]. %3D - Finding the extrema of f(x) =…

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Q: ´sin x-sin x cos x lim x2

A: This can be evaluated as follows:

Q: lim x → 0 sin^8 x / x

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Q: lim sin (2 – 2) cot² (x² – x – 2)

A: We have to find

Q: Calculate the value of the function f(x) = sinx cosx at  x= 0.1 using the 4th order derivative…

A: Here the given function is f(x) = sinx cosx, calculate the fourth order Taylor polynomial for the…

Q: Derivatives: using (4 step rule). 4. f(x)=sin3xcos3x 5. f(x)= x² cos(x² +1)

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Q: Using integration by parts, evaluate x cos(3x) dx x cos 3x - sin 3x + C Option 1 x sin 3x - cos 3x…

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Q: cos2x – sin2x cos2x For -dr=-F(x)+C What is F(x)? Cosx - sinx 2 3 2 sinx + -cosx+ cosx + - sin³x 3 3…

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Q: Consider the function on the interval (0, 27). x)8 sin(x) 8 sin(x) (a) Find the open interval(s) on…

A: Given function is

Q: Inverse identity Show that cosh (cosh x) = |x| by using the formula cosht = In(t + Vr - 1) and…

A: Given : cosh-1(coshx)=x for all x   and  cosh-1t=ln (t+t2-1)    Claim :…

Q: sin x x0 sin Vx sin (x2 + x) 26. lim 28. lim sin (Vx-3) 30. lim x - 9

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

Q: Continuity of a piecewise function Let For what values of a is ƒ continuous?

A: Given piece function is: fx=3sinxxif x≠0aif x=0 A function is continous at x=c if,…

Q: The Reciprocal Rule a. The Reciprocal Rule says that at any point where the function v(x) is…

A: Given: (a) The quotient rule is given as,

Q: sec3(In x) + sec²(In x) tan(In x) dx Given: 2x Find: du V sec (In x) + sec²(In x) dx tan(ın x) dx…

A: On solving this we will get

Q: QI Find f'(x) for 1+ sec-(x) S(x) 1- csc-1(x)

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Q: evaluate the limit.

A: Given integral is When x=0 Therefore, by applying L'Hopitals' Rule, we have

Q: sin x 25) lim x→0 5x 3(1 – cos x) 26) lim sin x (1 – cos x) 27) lim 2x2

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Q: The Second Derivative Test Use the Second Derivative Test to locatethe local extrema of the…

A: Given function is  (A) fx=3x4-4x3-6x2+12x+1  and x∈-2, 2 Differentiate the fx with respect to x.…

Q: QI Find f'(x) for 1+ sec1(x) (x) = 1- csc-1(x) -csc (x) + sec (x) csc '(x) + sec '(x) V(x? - 1)(1-…

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