"e" (Edexcel A-Level Mathematics): Flashcards

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"e"
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What is the approximate value of the number ee?

ee is approximately equal to 2.7182818282.718281828.

What is the result of differentiating exe^x?

The derivative of exe^x is exe^x.

How do you solve ex=ae^x = a?

Use the natural logarithm: x=ln⁡(a)x = \ln(a).

What is the gradient of y=ekxy = e^{kx}?

dydx=kekx\frac{dy}{dx} = ke^{kx}.

What is ln⁡(ex)\ln(e^{x}) simplified?

ln⁡(ex)=x\ln(e^{x}) = x.

Is ln⁡(x)\ln(x) defined for x<0x < 0?

No, ln⁡(x)\ln(x) is undefined for x<0x < 0.

How do you solve ln⁡(x−4)=7\ln(x - 4) = 7?

x=e7+4x = e^7 + 4.

What is the mass formula for decaying substance A?

m=40e−0.132tm = 40e^{-0.132t}.

How long for mass to reduce to 10g10g from 40g40g?

t≈10.5t \approx 10.5 years.

How is ln⁡(x)\ln(x) related to exe^x?

ln⁡(x)\ln(x) is the inverse of exe^x.

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