Question 21 Suppose that is differentiable function and f'(r) 2 2r-1 for all are R. If f(0) = 1, show that for all r<0, we have f(x) ≤ 2²-a+1. (Hint: Apply the MVT.)

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Q: Solve using the elimination method. Also determine whether the following system is consistent or…

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Q: Find the Maclaurin series and find the interval on which the expansion is valid. f(x) = ln (1-x²)

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A: Given f(x,y)=9x

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Q: Identify the open intervals on which the function y=9x-18 cosx, 0<x<2pi is increasing or decreasing.

A: A function y=f(x) is said to be increasing in an interval a,b if for everyx∈ a,b, dydx=f'(x)&gt;0.…

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Q: [√² √sec²z - 1

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Q: (a) Find the linear approximation L(x) of 2 f(x) = x³ at x = 3 L(x) = x = 27. (b) Use L(x) to…

A: The given function fx=x23. To find the linear approximation of fx at x=27.

Q: Find the derivate of the function F(x) = x²(x²-8) a) C 2 6b) f(x) = (5x²³²-7) (6x + 1) F'(x) = c) 5…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

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A: Given: y=sin-16x+1

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Q: For a certain mammal, researchers have determined that the mesiodistal crown length of deciduous…

A: Given: Crown length (in mm) of the molar t weeks after conception L(t)=-.015t2+1.38t-7.1 To find:…

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Q: For the following function, a) give the coordinates of any critical points and classify each point…

A: The given function is: hx=2x3-24x

Q: 1. a. Consider the following graph of a continuous function f(t) on 0 ≤ t ≤ 10. 2 s(t) p/ 0 6 10 4…

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Q: implied domain for the following function. x^(2)-4x=5x-6y

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Q: Follow the steps below to find the nonnegative numbers x and y that satisfy the given requirements.…

A: Given  x + y = 160

Q: Find the derivative

A: We are required to find the derivative of (a) y=cos2tan1+x3(b) f(t)=3csc5πt-71-cotπt5-7

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Q: y' = xy³ (1 + x²)−¹/2, y (0) = 1

A: y'=xy3(1+x2)-12  dydx=xy3(1+x2)-12given  y(0)=1∫xndx=xn+1n+1+c

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Q: Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate this…

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Q: Find the volume of the pyramid with base in the plane z = -10 and sides formed by the three planes y…

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Q: Find the derivate of the functions: a) f(x) = -3x²³ -4 sxt9 · f'(x) = (6) g (v) = 3 2√² +5V-9 g' (v)…

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Q: Given ƒ"(x) = 6x – 5 - and ƒ'(−2) = −1 and ƒ(−2) = 2. Find f'(x) = and find f(2)=

A: We need to find out the value of f'(x) and f(2) for which the second derivative is given.

Q: 2 Functions f and g are defined by f(x)=2(3+1)₁³ ,x+0 and 1 g(x)==-=-3₁ X≠3 respectively. (a) Find f…

A: The given functions are:f(x)=23+1x ;    x≠0       and        g(x)=1x-3 ;     x≠3

Q: b) lim x² +8x+16 X-1 x²-16

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Q: A student drew the graph of y = f (c), y = f' (x), y = g(r), and y = h(x). Unfortunately, they…

A: Find the graph of y=fx and y=f'x.

Q: Find all the complex roots. Write the answer in exponential form. The complex cube roots of 16+16i

A: Given:  z = 16 + 16i

Q: let y = 3 x² + In x - ex find y' O 6x + (1/x) + ex O 6x - (1/x) - ex O 6x +1 + ex O none of the…

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Q: Consider the function f(x) Enter an antiderivative of f(x). Do not enter +c as part of your answer.…

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Q: The area under the curve of the function f, using the Riemann sum, will be exact if we let the n or…

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

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Q: Solve y'+y=ex, y (0)=1

A: Solution-

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surface the cone…

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Q: 14. The domain of the function is y 4 2 -4-20 2 4 x

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Q: Find the derivative of the function. -7x³ - 6 6x² +7 f(x)=

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Q: 4 Function f is defined by f(x)= √√x+1, -1<x<1 x-1, otherwise (a) Find lim f(x), lim f(x), lim f(x)…

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Q: The Fourth Gate You arrive at the fourth gate, feeling confident in your skills. "It is a good thing…

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Q: 1 3 I(t) = ²/³ - 5 ² + 3 2 +86 (0 ≤ t ≤ 10)

A: I(t)=13t3-52t2+86for critical numbers put I'(t)=0d dt(tn)=ntn-1d dt(constant)=0

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: A volume is described as follows: 1. the base is the region bounded by y = e³.5x, y = 3.5x² + 0.9…

A: Given,             A volume is described as follows:             1. the base is the region bounded…

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Q: Find the area bounded by the curvey = x² + x +4, the x-axis, from x = 1 to x = 3. 16 14 12 10…

A: To find the area bounded by given curves.