If n = 12 m (me N), prove that "C₂ (2+√3)² "Co- - + "C4 (2+√√3)4 n "C6 (2+√3)6 ·+···=(-

Q: [ (ax + b) c+b) dx = ○ / (ax + b) ² + C O O4a ¹ª (ax + b) ² + C O4a (ax + b)² + C O4 (ax + b) + C 7a

A: You must have basic idea about indefinite integral in order to understand this better.

Q: Suppose f(x) =1 - 3x and g(x)= √x+5. a.) Show that f(-1)= g(11). b.) Find x such that f(x)= g(4)

A: (a) To show: That f-1=g11. Given: The functions are fx=1-3x and gx=x+5. Calculation: Substitute x=-1…

Q: Differentiate y ' 1+ 1 ਕਲਿਜਲ z+Vi+va 1+

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Q: 4 find the difference quoitent of... f(x) = -√x-19

A: To find the difference quotient of the following function.fx=x-19

Q: S(12 ) for √2x + 2x + 2√2x+...

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Q: if f(x)=16x+3 find f prime of zero

A: The objective of the question is to find the derivative of the function f(x) = 16x + 3 at the point…

Q: Show that T (1-i) cos- +isin- 40 40 (81-8√3) 6 10 = -√2

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Q: ƒ(5x² + 4x³ − 2x + 1)dx 이름 +2 -를 +a + C 5 2 O x5 x5 + x²-x²+x+C O 20x5 + A O 20x³ + 12x² −2+ C…

A: Given, ∫(5x4+4x3-2x+1)dx

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: Determine the number of roots of the equation f(x) = In|x + 2x^2 - 5x + 1a for all real numbers a. -

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Q: Which polynomial function would have the end behaviour of as x→ too, Y→ co? a) f(x) = 7x³ - 8x* -…

A: Topic = Functions

Q: pk Ph (x)=k! T(m-k+1) (k+m+1) m X \x X

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Q: 1 a (a) div A₁ = CScanned with CamScanner √gaxk =(√8A¹) 1 (5) 9³4-2 √²) = gkr kr g Əx

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Q: A power function has the form: f(x) = c x x^k where c is any real number and k is an integer.…

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Q: in (4) d. [5in(x+6) - In(x) - In(x² - 25)]

A: Solve the expression

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Q: b) x ³/4 + 2x c) 2x d) how I solved it but I'm not sure: (2³+ al = 2 4 a) x ³/4

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Q: Express In (2) in the form a + ib. (Simplify your answer completely.) In(z) = BRITK In( 4√2 ) + 1 (…

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Q: x* (8) √**+/+ x2 dx =

A: To evaluate the given integral

Q: x Q3: Show that csch-¹ (²7) = coth-¹(x+¹) x-1,

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Q: find the value of x in (1/(3x+1))+(1/(x+1))=(1/(3x+1)(x+1))

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Q: Evaluate: L-¹{- (A) B Ⓒe²t (cosh7t + (D) (s+ 2)²-49 e-2tcosh7t 4 e-2t(cosh7t – sinh 7t) 4 sinh 7t)…

A: The objective is to evaluate L-1s-2(s+2)2-49 Inverse Laplace transform using table values:…

Q: (z+1)(z+6)(z+10) z(z+2)(z+3) 3. What is the residue of at z = -2 (z+3)(z–2)² (z+2)(z+6) 4. What is…

A: 3) Given f(z) = (z+1)(z+6)(z+10)z(z+2)(z+3) Then Res(z=-2) = limz→-2(z-(-2))f(z)= limz→-2(z+2)f(z)=…

Q: lef f(x) = x-2₁ g(x) = ³√x₁ h(x)=x4, and j(x) = 4x, Express oach of the function. given below one or…

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Q: Evaluate using the substitution method. √ dz 2x4 (6 +x5) 4 2 1 [(26²du) - 15 (6+23)² + = = + C +x5)³…

A: Given ∫2x46+x54dx

Q: Evaluate / dx.

A: To integrate

Q: Ir X(s) (++2) (214)" find L[(2t)] Select one: O a. L[¤(2t)] (s+4) (s2+16) O b. L[r(2t)]| (8 | 4)…

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Q: Find the inverse funclion of 5/2 FO)=(2x2 on the doman X20

A: Given function is f(x)=2x52  domain x≥0 find inverse of f(x)

Q: a rational number y=10.01 b) Assume an integer, b=2 from 111 to 9 I assume from the range (0, ³/25).…

A: Given, X~Uniformx-32, x+32

Q: る(4xナx)(10x2+x2-2

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Q: Evaluate x²(x³ +9)¹/² dx 2 +9)³/2 +C Nia O (x² +9) ³/2 +C O C(x² +9)³/2 O x³ +9+C

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Q: sin + = √2 6 My thoughs sin π 4 ✓ why ? = √21232 f/2

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Q: For any integer n > 1 find, Hint: Substitute x + √x² + 1 = = U 1 So " (x + √x² +1)″

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Q: 10) (42x-33)+ (7x + 7) Please write in Q(x)+r(x)/d(x) Form

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Q: Prove that In( +VI-X²³) = In ( ¹+ √1-x²) sech ¹(x) =

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