2. Determine the given function is continuous or discontinuous at t=-2 (t² + 2 t < -2 t = -2 t > -2 If f(t) = {6 t + 8

Q: - { S 1² – 3 if r -1 2. Determine the constant k such that the function f(r) is continuous at r =…

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Q: 2. Let f(x) = 2e# – 3x² /a, whose graph is given to the right. Sketch in the tangent lines to f(x)…

A: PArt A: tangent line at x=1   The derivate of the tangent line at x=1, Find the derivative of the…

Q: 4. Find the extrema of the function f(x) = Vx (x + 1) and the intervals on which its graph is…

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Q: If fx) is a continuous function on [4,7] and F(x) is an anti-derivative of f(x) such that F(4)=9 and…

A: Given f(x) is continuous on [4, 7] and F(x) is the anti-derivative of f(x)                 F (4) = 9…

Q: suppose f is a continuously differentiable function satisfying f(3)=6, and f'(3)=5. Find (f^-1)'(6)

A: Given f(3)=6, f'(3)=5  To find f-1'6 By the formula, f-1'x=1f'f-1x And we know that if f(a)=b then…

Q: Given the function f(x) = {2ª 2x x 2 which statement is FALSE at x=2? O The derivative from the…

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Q: Define h(2) in a way that extends h(t) = (t2 + 3t - 10)/(t - 2) to be continuous at t = 2.

A: Consider the given the function,

Q: For which x value does f (x) = x - 3x2 + 1have a local maximum. CO C-1 C 1 C -2 C 2

A: Given: The function fx=x3-3x2+1, To find: point of Local maximum

Q: The function f(x) = e + e has a relative extremum at Select one:

A:

Q: Determine the values of x at which the function in Figure 18 is: (a) dis- continuous and (b)…

A: (a) Here from the graph, we can see that, The graph has a break at the point x =1, that is, Thus…

Q: A. Consider the function defined by [x² +1, if x<5 f (x)={ |6x– 4, if x25 a. Is f continuous at x =…

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Q: Let f be a differentiable function such that f(4) = 3 and f'(x) = -3x + 3. What is the approximation…

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Q: Suppose f is a continuous function where f(7) = 9 and f'(7) = 6 . The tangent line to the graph of y…

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Q: 1. Discuss the continuity and differentiability of the function g(t) at t = 1, where t3, t 1.

A: Given that : g(t)= t3,  t≤1t  ,  t&gt;1.  Let us check the continuity at t=1 :…

Q: Define g(t) = (1 + 21/t) -1 for t ≠ 0. How should g(0) be defined to make g left-continuous at t =…

A: Here given function as gt=1+21t-1or gt=11+21t Consider g(x) is left continuous at x=0 Thus…

Q: 1. Find the discontinuity point/s of f(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 2. Supposethat f(x)=?βx? −3 if βx + 2 ifx≤2 x &gt; 2Find the value of β so that f(x) is continuous…

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Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

Q: Consider the following equation below f(x)=4x^3+12x^2-96x+6 a.) Finally intervals on which f is…

A: Given:fx=4x3+12x2-96x+6To find:→Intervals on which fx is increasing→Local minimum and maximum values…

Q: Let A(x) f(t)dt, with f(x) shown in the graph below. -3- ** * T?

A: As per the fundamental theorem of calculus, given a function A(x)=∫0xf(t) dt, the derivative of this…

Q: 14. Consider the function f (x) = x²e+x . f(x) has two inflection points at x = _ and x =_.

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Q: For all but two choices of a, the function (x) x if x a will be discontinuous at the point x = a.…

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Q: Let f(x)=4x^2-2x-2 find the following: 1) f(x+h)= 2) (f(x+h)-f(x))= 3) lim h→0 (f(x+h)−f(x))/h 4)…

A: We have to find 1) f(x+h)=2) (f(x+h)-f(x))=3) lim h→0 (f(x+h)−f(x))/h4) Find the equation of the…

Q: make a sketch of the given function on the interval[0,∞).

A: Given: To Plot:

Q: Find the absolute maximum and absolute minimumvalues of  f on the given interval.

A:

Q: (a) The cost of producing 5-gallon water bottles is given by C(q) = 0.005q? + 2q + 1000. If 2000…

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Q: Determine all critical points for the function. T(x) = x3 - 3x? + 8 O A. x= - 1 and x = 1 O B. x= 0…

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Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

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Q: A continuous function y f(x) is known to be negative at x = 2 and positive at x=7. Why does the…

A: Given that f(x) is a continuous function.

Q: 5. Suppose the function g is defined by g(z) = { kz+1 for 0 < x< 3 for 3 <r < 5, mx + 2 where k and…

A: Given function is g(x)=kx+1  ,0≤x≤3mx+2 , 3&lt;x≤5 limx→3-f(x)=limx→3-kx+1=2k…

Q: Q3) If the function (2x + 1 +2 x > h) XSh f(x) having limit at x = h. Find the value of h. Q4) f(x,…

A: Our objective is to solve the above questions.

Q: if x1 O No, since g(x) is undefined at x=1. O Yes, and g'(1)=3. O Yes, and g'(1)=8. O No, since g(x)…

A: Given

Q: (2) h *.17 {, if t 3 Find a value of A such that the function f(t) is continuous for all t. 2 0 1.5…

A: To solve this problem, we  use the defination of continious function

Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

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Q: Suppose h(x) = [,f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) -4-…

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Q: d. If x=c is an inflection point for f, then f(c) must be a local maximum or local minimum for f.…

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Q: Find the linear approximation L(x) of the function f(x) = (1-x)1/2 at a=0 and then use L(x) to…

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Q: (a) At 12 noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/ hour and ship B is…

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Q: Suppose F(x) is a function with F '(x) = g(x). It is known that E(1) = 8 and that 9*)dt = –6 has a…

A: Please rate and feel free to ask any query about any part of the question.

Q: If f(1) = 13, f' is continuous, and f'(t) dt = 28, what is the value of f(4)?

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Q: If f(x) = then f (x) at z = 1 is

A: Given that :-         f(x)=1x         f'(x)=? at x=1

Q: Consider the piecewise-defined function Ax if x 0 h(x) е (a) Give values for A and B so that h(x)…

A: Given Data: Function: hx=Axif x≤0e-1/x+Bif x&gt;0 (a) The condition for the continuous function is,…

Q: Locate and classify all the critical points of the function.(If an answer does not exist, enter…

A: We need to classify all the critical points of the given function.

Q: (a) The cost of producing 5-gallon water bottles is given by C(q) = 0.005q² + 2q + 1000. If 2000…

A: As per the guidelines we are entitle to solve only three parts of first questions. So, I am…

Q: Suppose f(x) is an invertible differentiable function and the graph of f passes through the points 1…

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Q: Use differentials and the graph of f to approximate    (a) f (1.9) and (b) f (2.04).

A: