Find the coefficient of x10 in (1 +x+x²+x³ + •..)" Find the coefficient of x' in (x +x6+x² + • · ·)§. Find the coefficient of x7 in (1+x² +x+)(1+x)™.

Q: Prove that (-1ti3)" + (-1-is3)" has either the value 2n+' or the value -2" if r is any ). integer…

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Q: value of ∑n=1∞(6an+9bn) if ∑n=1∞an=8 and ∑n=1∞bn=2.

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Q: 1.] x5 +x* – 2x3 + x + C 7 2.]x3 +x² – 4x + C 2 3.] –+ C x2

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Q: Proved Ax (BNC) = (AX B)n (AXC) %3D

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Q: What is the coefficient of x16 in (2+x³ – xª)7 ? -

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Q: Find the GCF of -3x3 + 15x² – 6x

A: To find the GCF of -3x3+15x2-6x

Q: 12 Find the independent term of x in development (x² − ¹)²

A: We have to find the independent term of x in the expansion of (x2−1x)12, we'll use the binomial…

Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

Q: 16 Evaluate x1² (x4 – 2x² + 1)²dx. - 81

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Q: 15- (x + 5)lnxdx =? a) (-21/4) - 12In4 b)O (21/4) - 12ln2 (23/4) - 12ln4 d) O (-23/4) + 12ln2 e)…

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Q: What is the coefficient of x²x²3x4 in (x₁ + x2 + x3+x₁)?

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Q: is o(x). Hint: Use ling divisim

A: Let consider  fx=x4+x2+1x3+1 To show that f(x) is O(x).

Q: If fx)x3x+1 then fx) (In x]3x (3x+1}x3x (2x+ In xr3x+ 1 3x13r 3 Inx 3x+13 In x

A: Note:Hi there! Thank you for posting the question. The first line in the image is not very clear.…

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

A: Solve the expression

Q: What is the coefficient ot x" in (x+3) '9? What is the coethicient et x? in the expanson ot lx +2) 4…

A: Binomial theorem expantion

Q: 36 6 10. Find the coefficient of x³6 in (x + x² + x³ + x² + x³ + x² + x² + x³) ³

A: To find the coefficient of the term x36 in the expansion of x+x2+x3+x4+x5+x6+x7+x85.

Q: given 7(x-1)=2(3x+2) prove x=11

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Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

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Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: Find the coefficient of x11 in (x2 - 3x) / (1 - x )4

A: Solution:

Q: 4. Prove that (2x+3y)(4x²−6xy+9y²)+(2x−3y)(4x²+6xy+9y²) is 16x³ equivalent to 1 for x = 0.

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Q: 2 S²3 (x²-3x+18) 9x-X³

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Q: 1) 2xyy = (y)2 +1

A: we have to integrate

Q: a) 1 (x-1)(x+2)(x+4)

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Q: fx)-Sx+2, xs4 %3D (Cx+8 x>4

A: If the function is continuous, then f(x≤4)=f(x>4) at x=4 So LHS i.e. (x≤4) at x=4 is…

Q: 7 [3-(2-5x)] + X= 4 (9x+2} +1+x/²

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

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Q: What is the coefficient of x9 in (x + 2)¹5?

A: Solution :- x+215Apply binomial theorem:  a+bn=∑i=0nnian-ibia=x,  b=2=∑i=01515ix15-i· 2iExpand…

Q: 8.) (x-16) (x+ 4)

A: Our Aim is to simplify the expression x2-16÷(x+4)-(i)

Q: What is the coefficient of x in (x-3)7

A: To find the coefficient of x4 in (x+3)7.