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How to prove that (from i=0 to n)Σi^2= (n/6)(n+1)(2n+1), by induction.

First you must show that the statement on the right hand side is true for n=1: Σ i=0 i 2 when n=1, is equal to 1 2 =1 (1/6)(1+1)(1+2)=(1/6)(2)(3)=1 This means that the statement is true for n=1. Next you ass...
JB
Answered by James B. • Maths tutor
20794 Views

How do you differentiate X to the power of a?

To differentiate X a , where a is any real number, you multiply X by a, and subtract 1 from the power. i.e. d(X a )/dX=aX a-1
JB
Answered by James B. • Maths tutor
17653 Views

x^2 + y^2 + 10x + 2y - 4xy = 10. Find dy/dx in terms of x and y, fully simplifying your answer.

x 2 + y 2 + 10x + 2y - 4xy = 10 Start by differentiating both sides by x, the terms not containing y are differentiated normally, x 2 becomes 2x, 10x becomes 10, and 10 becomes 0. For the y 2 term, by implic...
GL
Answered by Guy L. • Maths tutor
15002 Views

Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?

y = e 2x (x 2 +1) 5/2 The first step is to calculate dy/dx. We can do this by splitting y into two parts and using the chain rule of differentiation: y = uv where u = e 2x and v = (x 2 +1) 5/2 . We now diffe...
AS
Answered by Adam S. • Maths tutor
13451 Views

Two lines have equations r = (1,4,1)+s(-1,2,2) and r = (2,8,2)+t(1,3,5). Show that these lines are skew.

Recall that for two lines to be skew they must satisfy two conditions: 1) They must not be parallel. 2) They must not intersect. We shall check each condition individually. Condition 1 The general vector equ...
DA
Answered by Dorian A. • Maths tutor
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