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Using the limit definition of the derivative, find the derivative of f(x)=sin(3x) at x=2π

First, we need to find the derivative f'(x) for all x, and then we will substitute x=2π into the function we find. To do this, we need to set up our limit:
f'(x) = lim [sin(3(x+h))-sin(3x)]/h as h-&...

Answered by Maths tutor
3755 Views

Expand and simplify (6x + 10)(3x - 2)

Expand by multiplying out the brackets (using crab claws or similar method): 18x^2 + 30x - 12x -20Simplify by combining like terms: 18x^2 + 18x -20

GC
Answered by Grace C. Maths tutor
3347 Views

Show by induction that sum_n(r*3^(r-1))=1/4+(3^n/4)*(2n-1) for n>0

Base Case n=1sum_1(r3^(r-1))=13^0=1=1/4+(3^1/4)(2-1)=1/4+3/4=1
Assume true for n=ki.e. sum_k(r
3^(r-1))=(3^k/4)(2k-1)
then for n=k+1sum_(k+1)(r
3^(r-1))= sum_k(r3^(r...

Answered by Maths tutor
3137 Views

Find the stationary points of y = 4(x^2 - 4)^3

This question challenges the student's ability to use the chain rule and to understand what a stationary point is. Having recognised that the chain rule is required, the first step is to use the substitut...

TL
Answered by Tom L. Maths tutor
3580 Views

Calculate the integral of ln(x)

Calculating the integral of ln(x) is harder than it might look and must be done using integration by parts, where the two parts are 1 and ln(x). The integration by parts formula is as follows
integr...

CR
Answered by Callum R. Maths tutor
2962 Views

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