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Integrate 2x^2 + 4

When we integrate, we raise the power by one and divide the term by the new power. So let's break the question down term by term. When integrating 2x² we raise the power by 1 to get 2x³

Answered by Eleanor F. • Maths tutor

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In a science experiment a substance is decaying exponentially. Its mass, M grams, at time t minutes is given by M=300e^(-0.05t). Find the time taken for the mass to decrease to half of its original value.

Firstly, calculate the initial value of of M, by substituting t = 0 into the equation M=300e^-0.05tInitially, M₀= 300e⁰=300 x 1 = 300When the substance mass has decreased t...

Answered by Bony R. • Maths tutor

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Differentiate, with respect to x, e^3x + ln 2x,

e^3x differentiates to 3e^3x as you multiply the function e^3x by the derivative of the inside function 3x. 3x differentiates to 3, so the answer is 3 multiplied by e^3x. The derivative of a natural log f...

Answered by Pelumi A. • Maths tutor

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Find the first derivative of 2x^3+5x^2+4x+1 (with respect to x)

In differentiation, your goal is to reduce the power of the terms that you're differentiating with respect to (in this case, x).The method for doing this is:Multiply the power of your x term by its coeffi...

Answered by Abigail R. • Maths tutor

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Simplify the following algebraic fraction; (3x^2 - x - 2) / ((1/2)x + (1/3)).

First we need to factorise the numerator into two expressions. We can see one expression must start (3x + ?) and the other therefore must hold (x + ?), we know this because the two bracke...

Answered by Bobbi L. • Maths tutor

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