For a submarine cable, the range of signalling is governed by the function f(r) = r² In (=) where 0

Q: Find the antiderivative F(x) of f(x)=x/3(12x2-6), given F(1)=5

A: An anti derivative of a function f is a differentiable function, whose derivative should be equal to…

Q: Find the absolute extrema of the function on the closed interval.

A: Differentiate the function h(t)=tt+3 by using the property…

Q: 3) Let f(x) represent the path of a particle. x* 1 f(x) =+ x 2 1 16 2x2 Suppose the particle starts…

A: The arc length = the distance covered along the curved path f(x).  A = the arc length  A =…

Q: 1+х f[X_, Y_] := 2 у - 1-x (1+) (у-1)2

A: We will use basic knowledge of the functions of several variable theory to answer this question.  We…

Q: The graphs above are approximate graphs of f and f' for f(x) = x°(x – 12). So f is decreasing (and…

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Q: For the function f(x) = 21² + 1, it is given that 3 f(x) dx = 21. At what value C does the function…

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Q: For what value(s) of x is f(x) = 4?

A: The first thing we must do for this case is observed the y coordinates for a given value of x…

Q: 9. If f(5) = 10, f ' is continuous, and f '(x) dx = 15 18, what is the value of f(6)? %3D f(6) =

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Q: Given the function f(x)=In(x² -4x+3) a. Find the domain of f(x) b. Find all x values where f (x) has…

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Q: Suppose that f: R→R is a differentiable function, satisfying f(4)=2 and | f(x) dæ=5. What is the 4.…

A: Integration by parts ∫uv'=uv-∫u'v

Q: Given that 7 < f(x) < 8 for 2 < x < 3, estimate the value of f(x)dx f(x)dx <

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Q: 2 Evaluate f(x) dx, given that f(x) dx = 6.

A: ∫abf(x)dx=-∫baf(x) dx

Q: Given the function f(x)=3x2. Use linear approximation at a=2 to estimate the value of f(1.99).

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Q: Given a function f(x) that is continuous and differentiable, and a point a in its domain, we…

A: This question can be solve by taking approximation as x tends to a (more close)

Q: What is the range of the function x) = X-3 O{xÎR|x'0} OIvIRly! 0} O tyÎRIy1 3} O{xIR|x'0}

A: Given function is                                         f(x)=1x-3 function is defined for all…

Q: (e) For wi at numbers x, - 2SXS 2n, does f(x) = 4? Where does f(x) = -4? f(X) = 4 for x =

A: The given function is: f(x) = 4sin(x) In the interval -2π≤x≤2π

Q: # Find a and b so that the function e-ax, x ≤ 0 f(x) = {₁² + 5x + b,x>0 is differentiable…

A: To find out the sum a+b.

Q: ind the critical points of the function f(x, y) = x² + y² + 10x – 9y + 3. List your answers as point…

A: In this question, concept of critical points is applied. Critical Points The critical points of a…

Q: Given the function f(x) =4x³– 39x²+90x +2, which of the following describes its absolute extrema at…

A: Given that, The function is following, f(x) = 4x3 - 39x2 + 90x + 2 We have to find the absolute…

Q: For what value(s) of x is f(x) = 3?

A: given :  f ( x ) = 3  find value(s) of x = ?

Q: At which r-values is the following function g differentiable? Explain and compute, where necessary.…

A:

Q: If f is an even function, why is S", f(x) dx = 2 f“ f(x) dx?

A: A function is said to be even if f-x=fx   We have to prove  ∫-aafx dx=2∫0afx dx   Consider left hand…

Q: 3 Given that 1 < f(x) < 2 for -4 < x < 3, find the best possible estimate of the value of f(x) dæ.…

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Q: cx +5 f(x) = for x 2

A: Explanation of the answer is as follows

Q: For function f(x,y) to have no extremum value at (a,b) is? 1) rt - s>0 2) rt – s?<0 3) rt - s? = 0…

A: To select: The condition for the function f(x, y) to have no extreme value at (a, b).

Q: For what value of the constant c is the function f continuous on (- o, 0) wh- cx + 7 if x 8 C =

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Q: Find the absolute extrema of the function on the closed interval.                      h(t) = t/(t +…

A: Given: The function h(t)=tt+3 and the interval [-1, 6].

Q: Given the function f(x) = x+5/x-4   Find the average rate of chnage of f on [x,x+h]

A: Given function:

Q: Given f(x)=2x2+4x+3, find the average rate of change of f(x) from x=−2 to x=t.Give your answer in…

A: The problem concerns the variation of the values of the given function over a given interval

Q: For the function f(x)=e5x+e−x defined on the interval(−∞,1], find all intervals where the function…

A: Find all the intervals for where the function is increasing and decreasing

Q: The cdf of checkout duration X for a book on a 2-hour reserve at a college library is given by: if…

A: We have given that the cdf, F(x) =  { 0,      if x&lt;0              x2/4 ,  if 0&lt;=x&lt;2…

Q: On which interval(s) is the function g(x) = xª – 8x² + 5 concave down?

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Q: The area of a disk as a function of radius is given by A = πr². How close must r be to 2.0 cm to…

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Q: is continuous and integral 3 to 1 f(x)dx =8, show that the graph of f intersects the line y=4 at…

A: Given that f is continuous and f13f(x)dx=8 To prove line y=4 intersects the graph of f altleast can…

Q: For f(x) = = 0 with xo = -2, find the estimated root using NRM if the stopping criterion-is…

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Q: For what value of the constant a is the function continuous on (-0, 0). for r 1 f(x) ax a =

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Q: If  f is continuous and  ∫09 f(x)  dx  =4  find∫03 xf (x2)  dx,

A: Given that,

Q: he graph of f(x) - x+1 is concave down on interval OA (-1,1) Ов. (0,1) Os. (-m 0LI(? m)

A:

Q: (b) If 38 10z f (2) = (2** + 6) e then at how many points the function f (z) is not differentiable?

A: f is every where differentiable, there are no points such that the function f(z) is not…

Q: 1 Is the function given by f(x) = ) 5x+1, for x s5, continuous at x= 5? Why or why not? %3D 5x- 19,…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: For f(t)= 0, cost, 0≤t<π/2 ΙΣπ|2 use the definition to find L{f(t)}

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Q: Find the absolute extrema of the function f(x) = x?e-z on the interval %3D

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Q: Suppose we know that f(x)dx = 2 and g(x))dx. S g(x)dx = 7, find the exact value of S°F (x) %3D

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Q: Find the lengths of the functions of x over the given interval. Approximate if necessary. y=e^x on…

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Q: Find the absolute extrema of fGx\=x. %½x°- 2 x+1 on the interval E1,2I.

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Q: For what value of p will r) be continuous? x-4 for x S2 %3D 2x + 3p for x> 2 f(x) =

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Q: Given that dy/dx = (x^2) and y=3 when x = -1, find the function f(x) in terms of x y-x+c--1 C

A: dydx=x23=x23

Q: On the graph of f(r) = tan z and the interval -T, 7), for what value of r does f(x) = 1? Choose all…

A: Givenf(x)= tanx , f(x)=1

Q: GIVEN: The function f:[0, 2]→ R, given by f(x) = x(x – 1)². Determine the value of c that is…

A: For mean value theorem:   If f(x) is real-valued function defined on [a,b] and   i) f(x) is…

Q: Suppose that f: R→R is a differentiable function, satisfying f(3)=5 and f(x) dx=8. 3 /x-s'(x) dx?…

A: