Find the constants a, such that the function g(x) continuous at a O O O a = Oa= 4 In 9 9 In 4 In 4 9 In 9 4 = 4. = J2eax 2 for x ≤ 4 In(x − 3) + x² for x > 4 is

Q: 1 nt) Consider the function f(x) = 6x2 +3 is concave up for x E isqrt6/6, infinity is concave down…

A: The concave up and down nature of the function is determined by the sign of the second derivative of…

Q: Find the divided difference f[x,x,. x2, x,], if A°f (x,) = 96 and h= 2. о а. 2 Ob. 1 3 о с. 1 o d. 3…

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Q: 9. State and prove the Mean Value Theorem for Definite Integrals by applying the Mean Value Theorem…

A: We have to prove the mean value theorem.

Q: Q6. Verify 02 f exDy Dyx for the function f(x, y) = x² sin2y + y²sin2x

A: A detailed solution is given below.

Q: Let f(x) = 2x In x. The approximation of f"(0.3) using the following formula with h = 0.1 is: %3D…

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Q: (f) p(xj,...X) =E

A: Degree is n.

Q: Let f(x) = ex²-1. The set f-¹([1, 3)) is: 75.5. O (A) (-√1+log 3, -1] U [1, V1 + log 3) O (B)[-√1+…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  we need to find…

Q: Find Lebesque integrae of function segment (-4,0) On f(x) = Txen X+4 O a. 12*41/3/5 O b. 3*41/3/5 O…

A: In R if a function is integral the lebesgue and Riemann gives same value

Q: Find the value of r*d(\x[³).

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Q: 3. (6れ)-) ANCTAN X (x+1) ² -y=ARCTAN

A: To expand the given function :

Q: Show that I [My |X] = 0 and var[My | X] = 0²M.

A: Solution :-

Q: show that the following function analytic f(z) = 4e²+ Sin Z arp

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Q: sech x dx , 0 < x < 1

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Q: Compute the Toylor serias about x= o of the function orcton (at -) up to t# terms of dlearee thre.…

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Q: Example 1: Determine the average rate of change between the points (-6,-2) & (3,8).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: A function f is defined on [0, 1] as follows : 1 f(x)=, when 1 <x< a <*< =1, 2, 3, ..) (r=. f(0)=0,…

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Q: Evaluate x* (1-x3)0/2 dx Select one: 3*1*3*1 , T 8*6*4*2 2 O None 3*1*3*1, T 8*6*4*2 4 7*5*3*1, T…

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Q: II (20’) Let X={1, 2, ., 16} and define function f(x)=rx for all x E X where rx is t remainder when…

A: Let X=1,2,.....16 defined by fx=rx  ∀x∈X We know that, "If a and b are two integers where a≠0 then…