Suppose that the functions q and r are defined as follows. =q(x)=−x r=-2x^2+1 Find the following. (r∘q)3= (q∘r)3=

Q: Use the chain rule to find the derivative of f(x) = 3(9z* – 82®)5 - You do not need to expand out…

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Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n =…

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Q: Find the derivative if w=(2x-7)-1(x+5)

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Q: Find f. - Vi- () -- 8. f'(x) = 9 %3D V1-x2 f(x)

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Q: An object attached to a spring oscillates around a position and is represented by the function…

A: Substitute value of 1 in y and solve for x.

Q: Verify that fy=f for the following function. "yx 5,3 6,4 f(x, y) = 2x°y³ - 8x°yª 5,4 = 10x*y³ –…

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Q: Find the constant a such that the function is continuous on the entire real line. Ax) = {2x2, (ах -…

A: Given that , the functionfx=2x2,x≥1ax-7,x<1We have to find constant a such that the function is…

Q: -x²+5 < f (x) < x+1 2

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Q: For what value of the constant c is the function f continuous on (-∞, 00)? cx2 + 2x if x 2.

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Q: Suppose that y is a function of x. Find if 2x°y 3 2y + 5. - -

A: We will find out the required value.

Q: Find the roots of the function f(x)=(2x-1)(x2+2x-3) with x belong to R

A: f(x)=(2x-1)(x2+2x-3)=0 We have find all the real numbers that make f(x)=0 because it is given that x…

Q: Suppose that z = f(x, y) is implicitly defined as a function of x and y. Determine for 4x²z³ - 5yz²…

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Q: of n'(x)= 2x-1/x2-x

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Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: 8 Describe the long run behavior of f(x) = x° – 5x* + 5æ° – 1 - - As x → - 0o, f(x) → ? As x → 0,…

A: Given  f(x) = x8-5x4+5x3-1 We have to find the end behavior of the function.

Q: For k(x)=(x−1)(−x2−2x)(2x−2), find the derivative of k(x) using the product rule. Do not include…

A: Obtain the derivative of the function k(x) as follows.

Q: Find (f-)'(a). f(x) = 4 + x2 + tan(Tx/2), -1 < x < 1, a = 4 %3D (F-1)'(a) =

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Q: when x # 1 Show that f(x)% = 2 when x =1 is discontinuous at x 1

A: Given query is to find the continuity of the function at x = 1.

Q: ,for x 1 Discuss the contuniuty of f andf'.

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Q: if cosh(x)=41/40 and x > 0, find the other hyperbolic functions of x

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Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

Q: Find the absolute extreme of the function on the closed interval y = 3cosx ; [0,2π]

A: To find the absolute extreme of the given function.

Q: Use the product rule to find the derivative. f(x) = (3x - 2)(6x + 1) %3D O f(x) = 36x - 4.5 !3! O…

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Q: 1 If f(x, у, 2)- ôf then х— у—3z ду а. 1 (х- у-3-)2 b. -1 (х-у-3-)* С. 1 (х-у-3-)° d. 2 (х - у-3-)?

A: In Partial differentiation w.r.t y we treat x,z as constants.

Q: Find the anti-derivative F(x) of the function f(x) = 2x - 7 with F(2)=55- %3D

A: We have to find the anti derivative of the given function following the given condition. anti…

Q: Find f'(1) for f(x) = In(v6x – 3).

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Q: Suppose f is a f(8(x))=2x² and differentiable function where 2x f'(x)=2+ f (x). Show that g'(x)=…

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Q: Find a function flx) such that f(x) -llex and %3D 3. f(0)-- 주

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Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

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Q: Differentiate the following f(x) =/20x- sin²(2x) Ox –

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Q: (b) Find the derivative of f (x) = (x² + 2) (8x − 5) by using the product rule. Let g (x) = x² + 2…

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Q: 8 — х — x2 if x 4 -

A: f(4-) = 8 - 4 - 16 = -12 f(4+) = 2*4 - 20 = -12 f(4) = 8 - 20 = -12

Q: Differentiate the following functions using product rule. 1. f (æ) = (3x – 9) (x – 6) 2. ƒ (x) = (æ³…

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx

Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

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Q: Find the derivative of f(x) = (5x 2 + 3x + 1) × (3x 2 + 2x − 1) × (x 2 − 1). Show all steps.

A: Given:f(x)=5x2+3x+13x2+2x-1x2-1

Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 22x + 4 if x ≥ 2on the closed…

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Q: + 2x if xs -1 if -1 1 f(-4), f(-}). (-1), f(0), f(25)

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Q: Determine f-¹(x) if 1 (X) = Or¹(x)=x2 X+2 X-3 X-2 or¹(x) X+3 Or¹(x)= X-1 3x + 2 3x + 2 X-1 OM(x)=)…

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Q: -4 - Find the derivative for the function f(x) = (5x−4+ 3x + 7) (8x−³ − 7x + 10) 5. Do not simplify…

A: Given, f(x)=5x-4+3x+78x-3-7x+105

Q: 4. If f(x) = sin x, show that f(2.x) = 2f(x)f(-x) %3D

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Q: Find a and b so that the function = { ax + b, 8x – 8x? + 4, ах + b, х -2 is both continuous and…

A: Continuity at x=-28-23-8-22+4=a-2+b-64-32+4=-2a+b-92=-2a+b→1

Q: Find the first 3 Iterates of the function f(x) = - 2x + 3 when x 3 =0 . 3, - 3, 9 - 2, 0, 2 2 z, -…

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Q: How should the function f(x)=x²-25/x+5 be defined at -5 to make it continuous at -5?

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Q: Find the slpoe of the secant line between the values x 1 =-1 and x 2 =3 for f(x) = 8x - 3

A: Givenf(x)=8x-3x1=-1  x2=3

Q: Examine whether or not the function fx' - 2r +1 ifxs 2 S (x)= x'-2r +1 [3x-2 if x>2 Is continuous at…

A: Given function, fx=x3-2x+1,     if x≤23x-2,            if x&gt;2 To find the continuity of the…

Q: C. Show that f(x) = (x26)² has no inverse on the interval (-∞,0).

A: Since you posted two questions here, i can answer only 1. Please reupload second question again.…

Q: For k(x)=(3x+2)(−x+2)(−3x2+x+1), find the derivative of k(x) using the product rule.

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Q: Find the derivative off(x) = 5(7x3−2x+ 1)−3.

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Q: What are the critical numbers of the function f(x)= 2x^(3)-2x^(2)-16x+1?

A: Let's find.

Q: Find the derivative by the limit process. Rx) = 4x3 + 2x2 %3D f (x) = %3D

A: Given: f(x)=4x3+2x2 To Find: Derivative by Limit Process. Concept: dfxdx=f'x=limh→0fx+h-fxh

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.