Exercise 2 Let a > 0. Show that for each k eN one has 2k(1-a) 2k+1 1 < 2k(1-a). ma m32k+1 2.

Q: Write p(x) = 375 -7³+57²-1 in the form of nested multiplication. Compare the computational cost…

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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: Find integers x and y so that gcd(3953, 1829)=3953x+1829y. x=2,y=5 x=-12,y=-13 x=-6, y=13 x=6,y=-13…

A: Solution:we have to find integers and so that first we find gcd of (3953,1829)here we see that…

Q: b) Find (3512, 2020) and find integers x and y such that 3512x + 2020y = (3512,2020).

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Q: Indicate the least integer n for which (3x6 + 2x2)(x3 + 3x) is O(xn).

A: Solution:-

Q: Find the term of (x² +x²)' that has x88 in it.

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Q: Find the coefficient of x24 in (x + x2 + x3 + x4 + x5 )8

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Q: For a, b E R, calculate (ax + b)dx (x²+1)²(x²+4)*

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Q: (8.9x10-17) + (1-599×10*15) =

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Q: 16. Show that (x + 1) is a factor of p(x) = x³ + 2x² + 3x +2

A: We have to show that x+1 is a factor of p(x)=x2+2x2+3x+2 .

Q: The city will pay to have soft pavement made of recycled tires installed in the playground. In the…

A: x=longer  side y=x-15=shorter side and the area is A=324 the area of the rectangle is given by…