22 If Sx) is an odd function, the second difference [SSAx) – 2(0) +-Ax)]/(Ax)? exactly equals f"(0) = 0. Why?

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives and fz = 44,…

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: The tangent line to y=f(x)y=f(x) at (−3,−2)(−3,−2) passes through the point (−4,−3)(−4,−3). Compute…

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Q: of f(x, y, tion of ve

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Q: 11. Use the Mean Value theorem to show that f(x) = 2x sinh (æ – 1) + 2" – x has a critical number…

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Q: As the denominator df goes down, the critical value of F goes ______ so that  ______ extreme value…

A: ANOVA(Analysis of variance ) is an extension of the t-distribution. When we cannot use t…

Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

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Q: Find (f - g)(x) if f(2) = 7x³ – 52² + 42x – 30 and g(z) = 7 O (f · g)(x) = 49zª + 269x² + 150 O (f·…

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Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

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Q: 2. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Is the function given by f(x) = 3x - 2 continuous at x = 5?

Q: 7. Is the function given by G(x) at x = 2? Why or why not? 1 x² - 6x + 8 continuous

A: Theory : If A function f(x) is continuous at some point a, then it must satisfy All of these…

Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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Q: #! Find f'cx) if fex)= Čx²+SX+2)(X-)

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Q: 8 Describe the long run behavior of f(x) = x° – 5x* + 5æ° – 1 - - As x → - 0o, f(x) → ? As x → 0,…

A: Given  f(x) = x8-5x4+5x3-1 We have to find the end behavior of the function.

Q: 4. Why is f'(x) approximated well by the difference quotient when Ax is very small?

A: Derivative of function f by definition is: f'x=lim∆x→0fx+∆x-fx∆x This is the difference quotient…

Q: Suppose J. 3sf(x)s5 for 2sxs8, how small can f (8) possibly be if f(2) = 10? State necessary…

A: Given that         3 ≤ f'(x) ≤ 5  for  2 ≤ x ≤ 8 Here we have to find how small value of f(8) can…

Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x&lt;4-x+7,   for  x&gt;4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

Q: Please show steps.

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x – 1) + 2" – x has a critical number…

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Q: X = (1-_-_-_-)* 2 o then f(x) tend:

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Q: 4.3. Show that the function f(x) = Ja² sin, if x 0, 0, if x = 0 is not of a bounded variation over…

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Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

Q: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

Q: What is the critical number c and function value f(c) of f(x) = (x – 2)² + 3x – 3. If necessary,…

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Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

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Q: 1 5. By using the cubic approximation of f(x) = --1 around a = 0 in question 4, estimate the error…

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Q: 4. In f(x) = {1– x² if -1sxs 1. Is the function continuous at x=1? Prove. (x² – 1 if x > 1

A: Given Function:                  f(x)={x2-1, if x&lt;-11-x2 if -1≤x≤1x2-1  if x&gt;1    To…

Q: If f(x) = etan-¹(x²) then f'(x) at x = 1 is equal to TU 2e4

A: The explanation of answer as follows :

Q: 3. Is the function given by (x²-4x-5, x<5 F(x)= x+1, x25 continuous at x = 52 why or why not ?

A: Given function, f(x)=x2-4x-5;x-5;x&lt;5x+1;x≥5; The objective is to tell whether the function is…

Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

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Q: In(8z) Siven f(z) the derivative f'(x) is 8. %3D O 8 8x o 1 O 78z 1 8x 1/8

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Q: 1. Consider the function f(x) = sinx - e-* has a root in the interval [0,1]. Use false position…

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Q: The rate at which the total average number of COVID cases is increasing at x=10 tents and dxdt=1…

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Q: Use Taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when 0.5 ≤ x ≤…

A: We have to use Taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when…

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives. In each case,…

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Q: [1, 2). over Calculate M6 for f(x) = 3 · In(x³) M6

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Q: 9. If f(x) = ], ( 22 - 5t-3 ]dt, on what interval(s) 0, is f increasing, decreasing

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: We use the quotient rule, product rule, and chain rule of differentiation to check the claim of the…

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

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Q: The tangent line to y=f(x) at (−8,−5) passes through the point (−3,10). Compute the following f(-8)…

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Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

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Q: 2. Consider the function а(т — 2) Vx +2 – 2 - if x 2, 2x 2 x² - where a, b, c are real numbers.…

A: Given function is  f(x)=a(x-2)x+2-2   if x&lt;2b                     if x=21x-2-cx2-2x  if x&gt;2…

Q: If F(X) is an antiderivative of *-2 + x-', then what is the value of F(1) - F(-1)?

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: 29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

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Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: 7, The inflection points of the function f(x)%= 글어 -금 + 12-음 ocurs at OCcurs at: ||

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