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remainder theorem

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What is the integratin of 1/sin2x?, ∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cos...

∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cosec2x - cot2x] + c = 1/2 log[tan x] + c Detailed derivation of ∫cosec x dx = ∫cosec x(cosec x - cot x)/(cosec x - cot x) dx = ∫(cosec 2 x

Differential equations, solve the differential equation 8yk+2-6yk+1+yk=9 ,k...

solve the differential equation 8yk+2-6yk+1+yk=9 ,k=0 given that Y0=1 and y1=3/2

Multiplication of two complex numbers, Multiply the given below and write t...

Multiply the given below and write the answer in standard form. (2 - √-100 )(1 + √-36 ) Solution If we have to multiply this out in its present form we would get,  (2 -

Reduced Row-Echelon Form, The augmented matrix from a system of linear equa...

The augmented matrix from a system of linear equations has the following  reduced row-echelon form (a)  How many equations are there in the system?  (b)  How many variab

How to add mixed numbers, Q. How to Add Mixed Numbers? Ans. If you...

Q. How to Add Mixed Numbers? Ans. If you have to add mixed numbers, you might try this method first: First rewrite the mixed number as a whole number plus a fracti

Types of infinity, TYPES OF INFINITY : Mostly the students have run across...

TYPES OF INFINITY : Mostly the students have run across infinity at several points in previous time to a calculus class. Though, when they have dealt along with this, this was jus

Example of infinite interval - improper integrals, Evaluate the subsequent ...

Evaluate the subsequent integral. Solution This is an innocent enough looking integral. Though, because infinity is not a real number we cannot just integrate as norm

Mechanical vibrations, This time we are going to take a look at an applicat...

This time we are going to take a look at an application of second order differential equations. It's now time take a look at mechanical vibrations. In exactly we are going to look

Prove that cos - sin = v2 sin , If cos?+sin? = √2 cos?, prove that cos? - ...

If cos?+sin? = √2 cos?, prove that cos? - sin? =  √2 sin ?. Ans:    Cos? + Sin? =  √2 Cos? ⇒ ( Cos? + Sin?) 2  = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒

Example of set theory, Suggest me the solution: Consider the given unive...

Suggest me the solution: Consider the given universal set T and its subjects C, D and E T = {0, 2, 4, 6, 8, 10, 12} C = {4, 8,} D = {10, 2, 0} E = {0} Find out

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