The gravitational force exerted by the planet Earth on a unit mass at a distance r from the center of the planet is GMr if r R .2 where M is the mass of Earth, R is its radius, and G is the gravitational constant. Is F a continuous function of r?

Q: -. For the function f, f '(x) =x² -1 and f(4) = -1. What is the approximation of f(3.9) found by…

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Q: Consider the function below. z²+4 z-2i z # 2i f(z) = (3 + 4i z = 2i Is f(z) continuous at z = 2i? If…

A: Let's solve.

Q: Let ​h(x)=​f(g(x)), where f and g are differentiable on their domains. If ​g(−1​)=2 and g′​(−1​)=7​,…

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Q: Let f(x) = Vx and L(x) be the tangent line approximation of f(x) at x =9. Which of the following…

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Q: If we have that f: R → Ris a continuous function , in which f'(7) = 6 and f(7) = -2 an equation of…

A: We have to find out tangent line

Q: Let A E R"Xn, let b e R", and let n n f (x) = xT Ar + 6Tx = Aikr;xk +> b;x;. i,k=1 i=1 Show that f :…

A: Definition: A function f:ℝn→ℝm is differentiable at x0 with derivative M if M:ℝn→ℝm is linear and…

Q: Let f : R → (−1, 1) be given by f(x) = x/(1 + |x|). Show that f is differentiable at x = 0, with…

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Q: Determine whether f(x) is differentiable at z = a (Justify your answer using the definition of the…

A: In the question we have to determine the function is differentiable or not.

Q: The function g(t) = \t| is differentiable at 0. True False

A: Given that g(t)=|t|We can write it as:g(t)=t   , t≥0-t , t<0

Q: If y = f(x) is an odd differentiable function defined on (-o, 0) such that %3D f'(3) = -2 then…

A: A function f(x) is said to be even if f(-x) = f(x) And odd if f(-x) = -f(x)

Q: Consider the function f(x) = a²e15z. f(x) has two inflection points at x = C and x = D with C < D…

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Q: Let f(x) ∈ R[x]. If f(a) = 0 and f '(a) = 0 [f '(a) is the derivative off(x) at a], show that (x -…

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Q: Find the values of a and b such that f is differentiable at r = 3 and then sketch the graph of f if

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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: Find the local linear approximation L (x)of the function f (x)= x² +3 at x = 1

A: Given that: f(x)=x2+3

Q: Let g(x) be a differentiable function such that g(−2)=0, g′(−2)=−5. Find the value of g(−1.8) using…

A: Given  g(x) be a differentiable function , g(−2)=0 g′(−2)=−5 a=-2 To find  g(−1.8)

Q: The derivative of f(t) = 21° · h(t), where fand h are differentiable functions is: A. 10° · h(t) +…

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Q: Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ] 3

A: Solution: The objective is to find the linear approximation

Q: If f is a differentiable function at a, then xf is differentiable at a and (af)'(a) is: Select one:…

A: We need to evaluate the following expression xf'a

Q: If a function f: D R is differentiable at a point (a, b)ED, then f is continuous at (a, b);

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Q: Find the maximum and minimum values of the function f(x) = x – sin x on [0, 27). %3D

A: The given function is: f(x)=x-sinx For maximum and minimum value, differentiate the function and…

Q: Let f(x) E R[x]. If f(a) = 0 and f'(a) = 0 [f'(a) is the derivative of f(x) at a], show that (x –…

A: Given: f(a) = 0, f'(a) = 0 [f'(a) is derivative of f(x) at a] To Show: (x-a)2 divides f(x) Concept…

Q: Find the absolute maximum for the function f(x) = re, x E [-1,3] %3D

A: Given :       function  f(x) = 12x2e-x       Interval  x∈ [-1, 3]    To find : Absolute maximum…

Q: Let f be a differentiable function such that f(-1) = 10 and f' (x) = x – 2. What is the…

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Q: Show that the subtangent of f (x) = ex is everywhere equal to 1.

A: Formula to find the subtangent of the function helps to find the required subtangent. Derivative of…

Q: If f(x) is a twice differentiable function with •1 f(0) = 5, f(1) = 4, f'(1) = 2, Then So 2x f"…

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Q: Find f'_(0) and f'„(0) for the given function f. (If an answer does not exist, enter DNE.) if x 0…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Question number 44 please

A: Given the function is:

Q: f(x + h) – f(x) - Let f(x) = 2.2x2 – 5.8x. Using the formula, m = estimate the slope of the h…

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Q: (c) Does there necessarily exist a differentiable function h with 0 < h(x) <1 and E = {x : h(x) = 0}…

A: Sol:in the given question we have to tell about the differentiable function f(x)s.t whose range is…

Q: Calculate the approximation of My for the given function and interval f Cx)=フメーンLュ,3 %3D

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Q: Let f(x) = Vx and L(x) be the tangent line approximation of f(x) at x =9. Which of the following…

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Q: 46. The gravitational force exerted by the planet Earth on a unit mass at a distance r from the…

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Q: Let f(x) be a differentiable function such that f(3)=12, f′(3)=−2. Estimate the value of f(3.5)…

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Q: If f"(c) = 0, then f(x) cannot have a local extremum at x = c.

A: We know, if f"(c) is negative then f(x) have local maximum at x=c and if f"(c) is positive then f(x)…

Q: Given a function f(w, x, y, z) = 2(w + 1)² x − xe²+, which of the following is not part of the total…

A: Given a function fw, x, y, z=2w+12x-xez+y2zw, to determine which of the following is not part of the…

Q: ar +b. 2r' - 1, f(z) = I>3

A: The given function,fx=ax+b,x≤32x-1,x&gt;3

Q: Let f be a differentiable function such that f(3)= 2 and f'(3)=5. If the tangent line to the graph…

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Q: Show the function f(z) = 1+2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: Consider the function z = f(x,y). If fx(a,b) and fy (a, b) both exist, and they are equal, then the…

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Q: Given the function f(z)= zz, Show that (i) the function is differentiable at z=0 and nowhere else.…

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Q: Let f(x) = Vx and L(x) be the tangent line approximation of f(x) at x =9. Which of the following…

A: We have to find L(x).

Q: Suppose it is known that for a given differentiable function y = f(æ), its local linearization at…

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Q: Every cubic function (i.e. function of the form f(x) = ax³+bx²+cx+d with a, b, c and d constants,…

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Q: Verify the condition of Rolle's theorem for the function y = f(x) = e xe[-1] ] f'(c) = 0 and find C…

A: Rolle's theorem: If f(x) is a real-valued function defined on a,b such that; 1). f(x) is continuous…

Q: 10.3.13. f(x, y) = xy ln(x² + y²).

A:

Q: The average revenue is defined as the function R(x) R(z) = (x > 0) Prove that if a revenue function…

A: Given average revenue defined as function R¯x=Rxx   x&gt;0 To prove if a revenue function Rx is…

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

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.