If r(x) is a function that counts number of prime numbers, then find the n(36.8) A) 10 B) 11 C) 12 D) 14

Q: Apply Rolle's theorem for the function f(x) = 8x² – 32x + 24 over the interval [1,3]. %3D

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Q: Consider the function f(x) = xn , where n is odd. Does f −1 exist? Explain.

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Q: 9 Find all the criticonl numbers of tthe function 3. メ2+メ

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Q: Consider the function: 81x2 + 16 f(x) = Ston 1 of 2. Cind alL cciticaL Soparats pauleiple with

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Q: 3. Find and sketch the domain of f(x, y) = In(9 – x² – 9y²). [Hint: In(x), x > 0]

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Q: 6. Use an appropriate substitution to prove f(r)dr = f(a + b – x)dr. %3D

A: We have to prove definite integral property.

Q: . Use the definition of error function, prove that [²' ( ²² ) = √T z

A: On solving this we will get

Q: Let f : R" → R with f(x) = /1+ ||x||?. Show thatf€ C.

A: As per the question we are given a multivariate function f from Rn to R , and we have to show that :…

Q: Verify that Rolle's Theorem can be applied to the function f (#)= =3 – 722 + 14x – 8 on the interval…

A: Solve the problem using Rolles theorem

Q: Evaluate the function f(x) = e* + In (x + 7) at c, where –7 < c < 6.

A: Given information : f(x)=ex+ln(x+7) 'c' lies between -7 and 6

Q: 13 Give the six circular function of 4.

A: To find: The six circular function of 13π4 (θ=13π4)

Q: Find the domain of f(x)=x² for 0<x<5. O (1,25] O (0,25) O [0,25] O [1,25)

A: Given: The function is fx=x2 for 0≤x≤5. To find: The domain of the given function. The given options…

Q: Q/Find the fartiel differe ntial Cquetion by elimineting the arbitrary function

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use Eceler's formula to express the function:7x) =xarsinx as the sum of a real andd imaginary…

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Q: let f(x) =x2 , on interval 0<x<2n, sketch

A: We have to sketch the graph of the function f(x)=x2 on the interval 0≤x≤2π.

Q: For the function f: (0, 1) → R, f (x) = 2"x+ {2"x}, (n, m e N; n > m), the number of points of…

A: Let's find.

Q: Find the constant a, or the constants a and b, such that the function is continuous on the entire…

A: Given function is f(x)=x3, x≤2ax2,x&gt;2

Q: What is T3 centered at a = 3 for a function f such that f (3) = 9, f' (3) = 8, f'' (3) = 4, and f'''…

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Q: 4. Use the definition of "f(x) is 0(g(x))" to show that 2* + 17 is O(3*).

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Q: Use the function f(x) = Vx and a starting point of a = 8 with linear approx- imation to approximate…

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Q: Suppose that f is a function such that f' (c) = 1 for some number c in the interval [a, b]. Is it…

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Q: #3) Determine whether the funchon 2XZ72 iS oto if = @ f(min)= m+n © f(mm) = m-n O f(m, n) = lni @…

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Q: Let f(x) = Vx. Compute the difference quotient for f at a = 7 with h = 4. %3D %3D

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Q: Find a point c satisfying the conclusion of the MVT for the function y(x) 4x2/3 %3D on the interval…

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Q: Use the linear approximation of the function f(x)=sqrt(9-x) at a=0 to approximate the number…

A: We know that the linear approximation of f at a is L(x)=f(a)+f'(a)(x-a). Here, f(x)=9-x and a = 0.…

Q: Find the intervals on which the function f(x)=x3+ax+b (where a,b are any real numbers) is convex…

A: Given function is firstly, we find f''(x)

Q: Compute f.F. dr, where F(x, y) = (2+ 12x²,9xy² ) and C is a line segment from (0, 0) to (1,2). (Use…

A: To Determine: Compute ∫cF.dr,where Fx,y=&lt;2+12x2,9xy2&gt; and C is a line segment from 0,0 to 1,2.…

Q: Find the domain: f(x) = In(3 – x).

A: A function is a relation which maps each element in its domain to exactly one element in its range.…

Q: Use the IVT to show that f (x) = x3 + x takes on the value 9 for some x in [1, 2].

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Q: 3. Determine whether the functions e2a and xe2 by calculating Wronskian.

A: Let f(x) = e2x and g(x) = xe2x Then,  f'(x) = 2e2x ,and g'(x) = e2x+2xe2x (by using chain-rule of…

Q: 2. Let f: [0, o0) R be the function given by f(r) x2 + 2. Is the statement Vrvy((f(x) > f(y)) → (x >…

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Q: Describe the long run behavior of f(2) = - z As z + - 00, f(z) + ? As a + 00, f(æ) → ?

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Q: Find the first 3 iterates of the function f (x) = 0.75x when 0 = 5. O 5, 3.75, 2.8125 O 3.75,…

A: To get the next iterate, apply the function f(x) to the previous  one.

Q: what valu e shouled be assigneed to a to make the function fex)= %3D 2ax

A: For the function to be continuous, the necessary condition is LHL=RHL=f(3) Here,  LHL=limx→3-f(x)…

Q: what should n be if f(x) = Xn defineof a polynomial function?

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Q: Find C for f(x)=x at a point of (1, 2) O 1/2 О 32 O 5/2 O 5/3

A: We need to find the constant after integration.

Q: Let f(x) = Vx . Compute the difference quotient for f(x) at a = 37 with h = 33

A: GIVEN f(x) = xDIFFERENCE QUOTIENT IS GIVEN BYf(a+h) - f(a)h

Q: Consider the function f(x) = 8+ (In(z² – 4))* What is its domain and range? (Use interval notation:…

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Q: Suppose f(x) = 4nx?e-Tx -e-n for all x € R. Show that f = -f. %3D

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Q: Consider the function y = 4ex + 7. What is the exact value of C in the interval [0, 5] such that…

A: We need to find value of C.

Q: let f(x) = on interval 0<x<2n, find a 2

A: See the attachment

Q: O Show that the function f: N2 N defined by f(x, y) = 2X3Y is injective but not surjective.

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Q: Use this definition to find f'(a) at the given number a. f(x) = V6x + 7,

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Q: (d) Justify whether f(A) compact.

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Q: Find the domain of the function f(x) = In(In(5x-19)). %3D

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Q: If f(x)=x', find f'(x), f"(x), f'''(x). (Pls 2. use the definition method)

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Q: Find all solutims in 15e interval T or 27) bele 2c05メー3c0sX = -

A: Given: Find all solutions in the interval [0, 2π). The equation is:…

Q: Q: A- find for the functions: - In =) + In(3x2) = In(3) %3!

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.