If n = 12 m (me N), prove that "C₂ (2+√√3)² "Co- - + "C4 (2+√√3)4 "C6 (2+√3)6 ·+···=(−1)| 2√2 1+√3 n

Q: b) Rationalize the numerator of 1 1 √7(x+h) √Tx - h Simplify your answer to the form A = A " where

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Q: (4) Evaluate 1 z² + 4z - 5 J -dz.

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Q: 3x SG / (√²² - 36 - 5√6) dz- +6² √a

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Q: Find the quotient and remainder of (x' + 8x² + 19x + 13) ÷ (x + 3). A (x² + 11x + 52) R 13 © (x² +…

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Q: Show that Q(4 - i) = Q(1 + i), where i = √-1.

A: To show that ℚ4-i=ℚ1+i. That is we need to show that ℚ4-i⊆ℚ1+i and ℚ1+i⊆ℚ4-i. Here i=-1 that is…

Q: Find the exact value of (√ 13 + √2 + 7 / (3 + √2)) without the use of a calculator.

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Q: x = KISS Comb 3 2 15.708×10²³ ± √(15.708x10³)² - 4x150 (-7.5398x106) 2x 150

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

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Q: verify that 6A = 3(2A)

A: Here given  Thus

Q: 6. Explain why, in ten words or less, for u = 4r6 cos(60) and B = any finite box in R² max|u(x, y)|…

A: Observe that the given function harmonic in B, where B is any finite box in ℝ2. Indeed…

Q: 2sin(2x)=√3

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Q: - A) -16x-5-x-2/3 C) 3 4) Find: d 4 dx x4 5 -4/3 B) ਪ੍ਰੈਲ-5-1582/3 D) - 1 5-2/3 433 3

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Q: √(x³ + 2x² + x -5) e 2X dx

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Q: 8.Differentiate the following. Do Not Simplify. 6x-x² a) y=√√5x²-3x(5-4x)³ b) y=√1-3x c) y = (x¹ -…

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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: Find the quotient of (2√3+2i)(-4+i) 2 (1-√3i)

A: Solution

Q: rel= = 0A 15, x² = 4(4x² - 1) If, 2 Prove that, x = √√5 +√√3

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Q: 4 | (5a' + 4x")dr Find 3

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Q: 6572sinx 10

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Q: b) Rationalize the numerator of 1 1 √3x 3(x+h) h Simplify your answer to the form as h 0 J where A "…

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Q: A x² B --x-In Ix+11+ C x² 2 -x+ In lx+11+ C 5x²=² dx x+1 C x² D x² +x-In Ix+11+ C +x+ In lx+11+ C

A: The given integral,              ∫x2-2x+1dx

Q: 3x3-5x2+5 Different iate with respect to X. x2+1 (x²+1)2 Different iate with respect to x. x2-1

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Q: what is the coefficient of the fourth term of (1/x - 5) ⁴

A: First we calculate fourth term then we find coefficient of fourth term.