Let f(x) be the piecewise function -2x + k f(x) = { x² + 1 if x < 1 if x ≥ 1

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 9-x² lim x3 3x² + x³ 3

A: Please refer to the image below

Q: Evaluate: x²+x-6 lim T-3 r+3

A: Given; Limx--3 (x2+x-6)/(x+3).

Q: Use the graph of the function f shown to estimate the indicated limits and the function value. a.…

A: As per our guidelines we can answer only 3 subparts of the given equation, so kindly repost the…

Q: cosx√sinx dx =

A: Our Aim is to solve the question-(8) in which our aim is to evaluate the integral given…

Q: Calculate the average rate of change of the given function over the given interval. Where…

A: The given table is: To find the average rate of the change on the interval 2, 6

Q: K Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

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Q: Find all functions g: R → R such that (fg)' = f'g', or show that there are no such functions.

A: Given: f : ℝ→ℝ, fx=e2x3+7x and g : ℝ→ℝ such that fg'=f'g'. To find: We have to find all such…

Q: The graph of a function is shown together with the tangent line at a point P. y 6+ 5 4 3 2 1 1 2 3 4…

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Q: Given that the acceleration vector is a (t) = (−16 cos(—4t), −16 sin(–4t), 5t), the initial velocity…

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Q: B)Convert r = √2 cos(0-) to cartesian.

A: Given a polar equation as r=2cosθ-π4 We have to convert given equation in cartesian.

Q: So all part a,b,c,d are all = 7?

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Q: 1. For a certain drug to have the desired healing effect and be safe, the amount in a person's…

A: Concept: A geometric series is a series where every term has a constant ratio to its prior term. A…

Q: 1) s(x) = 2x − 4/x2 + x − 2

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 1. Given that lim f(x) = 4 x-2 lim g(x) = -2 x12 find the limits that exist. If the limit does not…

A: Given limx→2fx=4, limx→2gx=-2 and limx→2hx=0

Q: g y = Ge=²*² + c₂ e ²x + cze 2x X

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Q: If r(t) = −4ti + 3t²j - 8tk, compute the tangential and normal components of the acceleration…

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Q: Sketch the graph of the function f. -5x + 7 1 2 x² + 1 f(x) = = if x 1

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Q: 3ax²-4b x-0 cx³-2m Evaluate lim where a, b, c and m are constants

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Q: Ex)= Sin X -TXX<T Sinodd function cal 2 an=0190-0 f(x) = {busin II X Using the data, I need to…

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Q: A. Consider the following multivariable function z(x, y) where {a,b,c} are constant numbers. 1.…

A: Please see the below picture for detailed solution.

Q: Find the indicated limit, if it exists. (If an answer does not exist, enter DNE.) 10x4 - 3x² + 2 2x²…

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Q: Use the Limit Properties to find the following limit, if it exists. +9 6x 7x-9 lim Select the…

A: Topic= Limits

Q: Solve for G GS 9dx = (x + √y²-x²) dy

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Q: Researchers measured the average blood alcohol concentration C(t) of eight men starting one hour…

A: NOTE: Refresh your page if you can't see any equations. . t 1 1.5 2 2.5 3 C 0.34 0.26 0.2 0.14…

Q: 1. Find dy for the following implicit function: dx cos([y(x)]² + 1) = 2x. Note: y(x) means that y is…

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Q: 4. Show that there are no integers m and n such that 80 m + 76 n = 3.

A: We have given integers m and n such that  80m+76n=3 86m+76n=420m+19n Put 20m+19n=λ 80m+76n=4λ So ,…

Q: x x + x = 0 x + x 3

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Q: Evaluate the integral. S dx (8x-9)4 1 24(8x-9)3 1 40(8x-9)5 3 8(8x-9)3 +C + C + C 8 3(8x-9)4 + C

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Q: xJ xp XP s/1-

A: I have stated the used formula in the solution.

Q: Use integration by parts to evaluate the definite integral Answer: te-t dt.

A: Given  that ∫06te-tdt.To evaluate : the definite integral.Solution :∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx…

Q: y = (c1 + c2x + c3x²)e³x

A: Topic = Differential equation

Q: A={0,1,2} B=(2,0,1} C={0} D={2} In each pair of sets, state the relationship on the space provided…

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Q: Question 2 Given: 4xdx + ydy + xy²dx + x²ydy = 0, Find C if x = 1, y = 1 | = 2 Ln 2 + Ln 5 = C 2…

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Q: Rewrite the pair of functions as one composite function. f(t(2)) Please show using TI-84 Plus…

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Q: d. Imagine moving along the curve in the positive x-direction on the interval [0, 3]. Give the…

A: follow the proceduue given below.

Q: Q12: If x + y = 10, then the largest possible Q13:The absolute maximum value of A) has no absolute…

A: Since, we have been asked to solve question-(13) in which our aimis to find the absolute maximum…

Q: Three slopes are given. For each slope, determine at which of the labeled points on the graph the…

A: In this question, we have to match the given options of slope to the given point on the graph.

Q: If student 10 is not selected, then student 5 should be selected how can I represent this constrain…

A: Given If student 10 is not selected, then student 5 should be selected

Q: Give examples of concepts, priciples and formula of the mensuration of plane figures Please make…

A: Mensuration: It is branch of the Mathematics which deals with the measurements of length, perimeter,…

Q: 13. Bacteria Culture A culture starts with 8600 bacteria. After 1 hour the count is 10,000. (a) Find…

A: NOTE: Refresh your page if you can't see any equations. . assume that the population growth function…

Q: Find a multivariable expression for the area of the rectangle A(x, y) Let y = x², substitute in to…

A: We need to find the expression.

Q: Q(x)=5x^2-19x-4/2x^2-7x-4 Find the vertical, horizontal, and oblique asymptotes?

A: We have given  Q(x)= (5x2-19x-4)/(2x2-7x-4)

Q: dy Consider the differential equation secy + sin(x - y)=sin(x+y). dx Using separation of variables,…

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Q: Find a polynomial function with the zeros -2,3,5 whose graph passes through (7,144) f(x)=

A: Given, Zeros= -2,3,5 We know that polynomial function with three zeros a b and c is given by, f(x)=…

Q: Q2) Solve using Laplace Transform y" + 2y' +5y = et sin t where y(0) = 0, y'(0) =

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Q: a da + b db = 0.

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Q: a) Calculate the following integral: x² + x x³ + x²-x-1 dx

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Q: z = e = x (a₁ as 4x + c₂an 4x -X

A: Given :y=e-xc1cos4x+c2sin4x

Q: Consider the helix r(t) = (cos(-1t), sin(–1t), 3t). Compute, at t= 픔 A. The unit tangent vector T =…

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Q: B) 25 C) 24 D) 10 Q12: If x+y=10, then the largest possible product xy is A)50 D) 30 C) 14 obrolute…

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