Use the binomial theorem to prove the following: (6) + (1) + ... + (6) = 26. In (a+b)n use n=6, a=b=1. O e^(i* theta) = cos(theta) + i*sin(theta) O x = (-b+sqrt(b^2 - 4ac)) / 2a O c^2= a^2 + b^2 - 2ab*cos(theta)

Q: Srow that PrE

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A: Hi! Thank you for the question As per the honor code, We’ll answer the first question since the…

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A: note : Since you have posted multiple questions, we will provide the solution only to the first…

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A: To evaluate the integral.

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Q: 7) e* Cos 2x

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A: One method is by using formula and derive whole solution. 2nd method is direct method by using…

Q: Problem 3. Let a, b and n be positive integers. Prove that (a) gcd(an, b″) = gcd(a, b)” and lcm(a”,…

A: To prove the given statements, we will use the following properties of the greatest common divisor…

Q: Prove that E (2s+l)=3n" whenever 'nisa psitre r'nisa pisitive intger. 32.

A: Given that,      ∑j=n2n-12j+1=3n2, n is a positive integer

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A: Arc length of a curve between two points is the distance between the two points with the restriction…

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Q: 2. 2) tan- 1 4) sin- 6) tan-1 V3 -1 01_ V3 10) sin -1 2. 12) tan-! 3.

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Q: Note that 1/4 ≠ 1/2; but (1/4)^(1/4) = (1/2)^(1/2). Prove that there exists infinitely many pairs of…

A: We will first parametrize the equation : aa = bb  Then we will eliminate the trivial solution : a =…

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Q: Prove that: (1+ x)*** (n+ 1)x C. + + 2 3 n+1

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: a) Compute the quotient (22 + 2i) / (2 + 2i) b) Suppose z = (In 2) + i (pi/2). Compute e^z

A: " Since you have posted two questions, we will solve first question for you. To get another question…

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A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let p=17. If a belongs to F_{17} and a is non zero , compute the value of a^{16}(mod 17) for a=3 .

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A: Given- cosπ-θ=cosθ To Find- The sequence of the steps that verify the above identity. Identity Used-…

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