Define Jn(x) = x²n+¹In(x), for n ≥ 0 Exercise 2.1: Use the facts that Jn(x) 1)In-1(x) - An(n-1) In-2(x) to establish = 2n+1In(x) and x²in(x) Jn(x) = 2n(2n-1)Jn-1(x) - 4n(n-1)x² Jn-2(x) = 2n(n-

Q: Let h(x) = f(x)g(æ). If f(x) -3x? – 4x + 2 and g(x) = -x² + 3x +2, what is h' (-1)? Do not include…

A: Given, h(x) = f(x)g(x) f(x) = -3x2 - 4x +2 g(x) = -x2 +3x +2  We have to find h'(-1)

Q: The solutions of cosh(2x) = 8sinhx - 5 are a) x = ln (4+ √17) and x = ln (1 + in (1 + √2) b) x = ln…

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Q: The law of cosines. Prove this generalization of Pythagoras' theorem (see Figure 2.7): || X - Y||² =…

A: As per Bartleby answering guidelines when multiple questions are posted in single picture then the…

Q: Apply the special case of the general power rule d/dx [h(x)]2 = 2h(x)h(x) and the identity fg =…

A: dhx2dx=2hx·h'x  &  fg=14f+g2-f-g2

Q: (3)f(x) = x – [x]; 0x=5 (i) x=

A: Greatest integer function:  A function that results  in the greatest integer less than or equal to…

Q: J1(z) rove that J(x) = -J(z) and J{(r) = Jo(z)- %3D

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Q: Show that E(X-µ)³ = E(x³) −3 [E (x²) ][E(X)] + 2[E(X)]³

A: The linearity of expectation property: With the assumption that, Xi's (i=1,2,...n) with n positive…

Q: Find a formula for f (z) if f(z) = I+1 f '(z) =O ( )'(2) =D-

A: We will use concept of inverse function and differentiation of a function.

Q: x(n) = 3 [2n + 4″]

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Q: This answer is incorrect, could you please attempt it again?

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Q: ] 5. Consider h(x) = (x³ + 2)². (a) Expand h and compute h' using the power rule and polynomial…

A: Explanation of the answer is as follows

Q: g(x)=√(x² - 1)², find g'(x) O none of these answers O (2/3) (x²-1)-1/3.2x O (2/3) (x²-1)-1/3 O (2/3)…

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Q: Y= xy3x=5 (унуза

A: This is question of calculus  Here one equation is given  We have to decompose  it by apply both…

Q: Consider the polynomials a(x) = r' + x³ + x + 4 and b(x) = 2r³ + 4.x² + x + 2 from Z5[r]. a) Find…

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Q: (a) Let f(x) = In x and g(x) = Va. Show that f(x) and g(x) are both increasing when x > 0. (b) Let…

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Q: Find f (x). f(x) = 2 In (1 + 7x?) f(x) = %3D

A: f(x)=2ln(1+x2 ) Differentiating w.r.t x both sides, we have f'(x)=2ddx (ln(1+x2))…

Q: Show that the Maclaurin polynomials for f (x) = ln(1 + x) are

A: The given function is fx=ln 1+x. fx=ln 1+x f0=0 f'x=11+x f'0=1 f''x=-11+x2 f''0=-1…

Q: Let ​F(x)=x2−11 and ​G(x)=12−x Find ​(F•​G)(−5​)

A: Given,two functions F(x)=x2-11  and G(x)=12-x

Q: The region bounded by f(x) 2x² + 12x + 14, x = = 0 is rotated about the y-axis. Find the volume of…

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Q: LET • (CX)= In [x²(x+5) ³ (x² + 4)⁰7 f'(x) = LET F(x) = \n [X²(X + 3) ³ (X² + 2)²] Cico

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Q: The Gamma Function I (n) is defined by I (n) = xn-le-ªdx,n > 0. (а) Find Г (1), Г (2), and Г (3).…

A: We will show the given results.

Q: 10. y"of y = arc tan

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Q: -Vx2+5 -x f(x): f'(0)? -x+2

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Q: Find a formula for ƒ¯¹(x) if ƒ(x) = = (²+1)* ƒ-¹(x) = (-¹)'(z) =

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Q: Assume that (8) ∞∑n=1nanxn−1=∞∑n=0anxn∑n=1∞nanxn−1=∑n=0∞anxn for all x, and determine what this…

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Q: Find the first derivative of e O - (3x+2)e-³r x3 O (3x+2)e-31 x4 O(x-2)e-³x x3 O- - (3x²+2)e-3x x3…

A: To find the derivative of the given function.

Q: Let Use the chain rule to find f(x)|x=1 f(x) = √6x² + 9x + 4. d - f(x)|x=1· dx

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Q: Find In(x) – In(x² – 1) +2 In( +3) -

A: Our Aim is to find 13 ln (x) - ln (x2-1) +2 ln (x+3) -(i)