Explain why we can not easily evaluate expressions (a) sin r dr; (b) (updated) n² n³-1' NEZ\{1} Use Jordan's lemma (rather, the idea from its proof) to evaluate them.

Q: Question 8: a. b. 12 (5+3)*(S²+3) 18 (5+3)*(S²+9) 6s C. (s+4)*(s²+4) d. None of them L(sin…

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Q: I Find sin 0. B 1 (-7,-8) ?]√[

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Q: Apply Maclaurln's Serles to Show (-1)*-1,2=-2) 2(n – 1)1 cos X=

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Q: Which of the following is not an indeterminate form ? 33 8|800108 OO OO

A: Let's find.

Q: that "C₁ sin 2x + "C₂ sin 4x + "C3 sin 6x 1+ "C₁ cos2x+ "C₂ cos 4x + "C3 cos E x; where ne N

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Q: Do c only

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Q: 1+ex dx

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Q: 8- Evaluate a) Sz? + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) S 3x. csc² dx x3-9x2+8

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Q: i dont get why we take the step to show that ||x||||y||≥0 for all x,y in real numebrs

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Q: lim 84x 10" +5" 2" +5" 8" - 4" + sin(4") (−1)n +4"

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Q: lim, o (cos z)= takes which indeterminate form? А. 100 В. 00 С. оо D. Е. 1 х о 8 -18

A: Here, we can solve it by taking the limit of individual terms.

Q: Consider solving x²V1-x² dx using trigonometric substitution. Which of the following is true? a. 2…

A: In trigonometric substitution method, the variable is substituted with a trigonometric function to…

Q: tan °(ln z) sec® (In z) Evaluate dz.

A: Evaluate: ∫tan3lnxsec6lnxxdx

Q: Since P+ Q, it follows that [(a1 + a3 + a5) – (a2 + a4)] [(B1 + B3 + B5) + A (82 + B4)]' | P+Q =…

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Q: 9. Prove the following algebraic identity: (a - b)(a? + ab +b?)=a' -b'

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Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: Consider the fune tion fa)- In[ax- b an tb] where c= ? -6 bi 2ab ind f' ()

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Q: Solve the integral 10. (tan 2x + sec 2x)³dx

A: Given integral is: I=∫tan 2x+sec 2x3dx We have to find the value of this integral.

Q: de a+bcose' where a> bl. Hence or otherwise evaluate 2n de √√2-cose 3

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Q: 2. Which of the following is a root of (-1+i)š (a) V2 (cos165° +i sin 165") tbWZfcos65ª+tsimÓS“) (c)…

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Q: Evaluate L{3(sin² 2t )} 24 24 24s 24 а) s(s² + 4) b) d) s(s² + 16) s(s² + 16) s(s² – 16) a O Option…

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Q: Choose the integral that would find the area inside r =3 sin 0 and outside r = 2-sin 0. -1

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Q: sin n 3 4TC

A: The given trigonometric function sin4π3 Since sinπ+θ=sinθ

Q: 13. Write sin(tan-)) ; x > 0, as an algebraic expression of r. 49 + x² iv) 7 ii) 49 + x² iii) 49 +…

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Q: Step by step

A: We will need integration by parts for this problem. So we assume u and dv then find du and v

Q: Evaluate the following: 1) (1+ tan? 0) + iv1– sin? 6 2) (x + yi)? = 2 + 4i 3) (cos 20 – sin* 20) +…

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Q: sin- & cos(ma) + sin (md)] (cos 6-1) If F[ - 5 in 4 cos ( (m-1) 4) + Sin (cm-1) 1) ] = (Rcos 6-1) […

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Q: 6) (Зу)2 O 9y° O 9y O 6y O 6y° бу

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Q: 4) cos 20 = - 25 < 20 < T Find sin 0. A) 5 B) 10 7/2 D) - 10 Find the exact value of the expression.…

A: As per guidelines we have to solve one question

Q: 1) cos- 0 V3 3) cos-! 5) sin--1 7) cos-1

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Q: Find the following commutator Sin (kx)] a2 (b) x) 33 (c)x²]

A: The commutators are solved as shown below.

Q: Answer the following: a) If sin=-¹|2|<1/1 Prove |sin" = <sin"¹|=| < b) prove that -1 tan z = 8 Z z =…

A: Given: sin-1z&lt;π2   To prove: a) sin-1z&lt;sin-1z&lt;π2b)…