(5) =D4 arctan 239 1. Derive Machin's identity. [Hint: Put a = arctan(). From the relation tan(x +y) = tan x+tan y obtain 1-tan x tan y 4) = 1 119 and tan(4a tan 2a = , tan 4g = 12 239 120 From the numerical evidence 3. (a) 03 + 13 1 13 + 13 0³ + 1³ + 2³ 24 23 + 23 + 23 36 03 + 13 + 2³ + 33 108 33 + 33 + 33 +33 100 03+13 + 2³ + 33 + 43 320 43 + 43 + 43 + 43 +43 he deduce-as did Wallis–the value of the limit 13 + 23 + 3³ +...+ n³ to L = lim of n→∞ n³ + n³ + n³ + · . . +n³ Chapter 8 410 Use Wallis's method of partitioning by "infinitely (b) small rectangles" to find the area under the curve = x'over the interval [0, a]; in integral notation this amounts to calculating x'dx. y = x %3D a Va Vx dx. 4. Given Wallis's value for " x?dx, obtain y = x2 %3D (Vā, a) Vx dx Nā x² dx х Na 1 Gottfried Leibniz: The Calculus Controversy t

Q: If A = A−¹ . 9 7 1 0 1 5 00 01

A: The matrix is given byTo determine: The inverse of the given matrix.Formula used:

Q: Which graph correctly solves the equation below? -x²+1=x²-4

A: topic - quadratic equations

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A: Given that The power series fx=1-x-2x3-4x4                      1 and Chebyshev polynomials T0x=1…

Q: 27-3 Det A=-1 5 - 4 690

A: DetA=  2   7  -3-1  5  -4   6  9     0=+25-49   0-(+7)-1-4   6   0+(-3)-1  5   6  9…

Q: 8 + e = o %3D

A: Given equation is  x + y + e^xy = 0

Q: 3. Identify all the cycles at each node of the directed graph above.

A: Cycle is defined as a path that start and end at the same vertex.

Q: A) Suppose F(xy)- М(х,у) і + N(x,y) j is a vector field on the xy plane such that F•dr = 0 Se I F•dr…

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Q: only one answer is correct

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Q: Add. 4 4a + 3

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Q: MAT

A: Graphical representation:

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Q: Answer key to this packet

A: We have to use the diagram and classify the angle pairs as vertical angles, adjacent angles,…

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Q: (5,19),(8,18),(10,14),(12,7) find the value of r and round to four decimals

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A: Given : (a3)(a-1)a9a31a-3

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A: We will find out the required value.

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A: Given: To Find: To find the slope of the following line segments:

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.