Let h(x) = x + |x|. Sketch a graph of y = Determine the values of x for which the function is differentiable. Find a formula for h'. (Hint: break it up as a piecewise function based on th obgolut e volu

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Q: Sketch an approximate graph of g onthe interval0<=x<=4 g(x)=\int_{0 }^{x}( f(t)) d t Identify…

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Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x -…

A: Given that f'(x)=x-12x+2

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Q: Let ƒ(x), g(x) be two continuously differentiable functions satisfying the relationships ƒ′(x) =…

A: Given,

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A: The graph of f'x is given as , find the absolute maximum value of fx over the interval 0,3.

Q: Given the function h (x) = : x+1 Over what interval(s) is h (x) decreasing?

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Q: Find a number a such that the tangent lines to the graphs of two functions f(x) = loga(x + 6) and…

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Q: - Is the function given by G(x) = Why or why not? continuous at x = 0?

A: We know that function is continuous only if its left hand and right hand limit equal, That is ,…

Q: 4. Find the value(s) of x at which the graph of the function g(x)=x'e has a horizontal tangent line.

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Q: 2. The graph of f'(x), the derivative of f(x) appears below. Use the graph to answer the following…

A: Consider the given information.  (a) The function f(x) will be increasing if f'(x)&gt;0. As, in the…

Q: 1) Draw a rough sketch of a continuous function, ƒ(x), with all the following properties: A) ƒ(0) =…

A: A) f(0)=4 , f(5)=-1, means that points (0, 4) and (5,-1) lie on the function B) f'(0) =0, f'(5)=0…

Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x –…

A: To find out the correct options.

Q: Let f(x) = x^2(ln x − 1) (e).Find the inflection point(s) of the graph of f, if any.

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Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

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Q: 2. Find a function of the form y = Asin(x) + D or y = Acos(x) +D whose graph matches the graph…

A: We know that time period of sin(x) and cos(x) both are 2π

Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x –…

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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: Q1 (a) Sketch the graph of two continuous function g(x) = cos x and h(x) = on the same plane,…

A: ..

Q: Q1. (a) Show that the following function is continuous at x = 1 for all values of p. spx + 1, if x >…

A: the given function is: fx=px+1     if  x≥1x2+p      if  x&lt;1 we have to show that the given…

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A: The graph of the function f(x). We have to estimate the integral ∫03f(x)dx.

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Q: Consider the conduction of heat in a rod 40 cm in length whose ends are maintained at oC for all t>…

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Q: Let y = f(x) be an positive increasing function defined for x > 0. The length of the curve described…

A: Given:         Length of curve y=f(x) is between x=0 and x=t is equal to14t4+t2+lnt+4+t2−ln2.

Q: Consider the following. (x) = e* + 3x Find an interval, of length 1 and having integer endpoints, on…

A: The given function is: f(x)=ex+3x

Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A: Concept: L'Hospital rule:Let f and  g be functions that are differentiable on an open interval (a,b)…

Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A: given,         limx→∞x3e2x

Q: On the graph of f(x) = tanx and the interval [ − π, π ), for what value(s) of x does f(x) = 1?

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Q: The graph of a function f is given. YA Estimate 10 [20 1 0 1 f(x) dx using five subintervals with…

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Q: Suppose that we know that the function f(x) is differentiable at = a, then what must always be true?…

A: We have to choose correct option

Q: Suppose that  f  is a differentiable function with  f (4)  =  ln 6 and  f ′(4)  =  3. Let h(x)  =  e…

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Q: Q1. (a) Show that the following function is continuous at x = 1 for all values of p. spx + 1, if x…

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Q: 35. Given that f(z) is a continuous even function, then A 0 D

A: We will use the definition of an even function and properties of definite integrals to find the…

Q: Suppose that h is differentiable and h(x + y) = h(x)h(y). Find a formula for h'(x)consisting of a…

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Q: Compute the first and second derivatives of the following functions of x. In each case, determine…

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Q: Let y=p(x) betheimplicit function corresponding to the equation f(x, y) = log(9) and such that p(3)…

A: As per the instruction, we will be solving part (d). Here, we have f(x, y)=logx2-y2+1. Let y=φ(x) be…

Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A: limx→∞lnx3x=limx→∞3lnx2·1x1    By using L'Hospital's rule=limx→∞3lnx2x=limx→∞3·2lnx·1x1    By using…

Q: Find the values of α and β such that the function f(x) =αcosx + 2 if x < 0  and f(x) = βe3x + αx2…

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Q: Find each value of x at which the graph of f(a) xe-2 has a horizontal tangent line. O = -1 only and…

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Q: 1 Suppose y : [0, x) →R is continuous and order exponential. If L{y} s3/2 %3D and y(0) = 1, express…

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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: At what values of x, if any, is the function shown below not differentiable? 5+

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Q: The graph of the derivative f' of a continuous function f is shown below. (Assume f' continues to…

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Q: function, that is 0 everywhere except at t=0, is know as:

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Q: 1. Find the absolute extrema for the following function over the given interval: f(#) = * - + 2 +2…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: The graph of f'(x), the derivative of a function f(x), is shown at right. Which of the following…

A: Use the concept of derivative of a function and check all the given options.