Search over 10,000 free study notes

First step: n=1 we have 8¹ -1=7 which is divisible by 7. Assumption step: 8^k-1 is divisible by 7. Induction step: Using the previous step we have that 8^k-1=7x. So 8^k<...

Using the general rule d/dx(a*x^n) = a *n * x^(n-1) and the linearity of the derivative operator, we obtain:
6x^5+20x^3+0 = 6x^5+20x^3

Draw a diagram of the graph y=sin x between the stated interval. Identify the two extrema. Required interval is in between the two points.

y= ln(4x-7)+18 y= a(x^2 +b)^1/2
At x=2 dy/dx = dy/dx and y =y
At x =2 y = ln(8-7) +18 y = ln 1 +18 y =18
At x = 2 18=a(4 +b)^1/2 18/(4+b)^1/2= a
y=ln(4x-7)+18dy/dx= 4/(4x...

a) Integrate the given expression using integration laws we have learnt to give [(x^4)/4 + (3(x^2))/2 + 2x ] and you do not need a +c constant as we have limits.b) Substitute the limits into the equation ...