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Find an antiderivative to the function f(x) = e^x cos(x)

We see a product of two things, so we should consider integration by parts (IBP). IBP is usually useful when either 1) you can differentiate or integrate one of the two things repeatedly to eventually get ze...
CA
Answered by Christoffer A. • Maths tutor
1610 Views

Solve inequality: sqrt(x^2) + x < 1

There are two possible solutions, substitution and using absolute value. Here, we will use absolute value method.By definition of square root we get: sqrt(x^2) = |x|. By definition of absolute value we get:|...
RF
Answered by Robert F. • Maths tutor
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Solve these simultaneous equations: 2x + 3y = 19 and x + 4y = 17.

By multiplying everything in equation 2 by 2, you get 2x + 8y = 34. If you then subtract equation 1 from this you get 5y = 15. Thus y = 3, going back to equation two, and subbing y back in, x + 12 = 17, ther...
JH
Answered by James H. • Maths tutor
4187 Views

Find the equation of the straight line that is tangent to the curve 2x^2 - 5x - 3 =0 when x = 3.

First differentiate 2x 2 - 5x - 3 to get 4x -5. At x = 3, the gradient of the tangent must be 7, and we know it goes through (3, 0) Plug the values into y = mx + c to get the equation of the line, which is y...
SL
Answered by Sarah L. • Maths tutor
3275 Views

Given f(x) = 7(e^2x) * (sin(3x)), find f'(x)

f(x) = 7e 2x sin(3x) Chain rule: f(x) = uv → f'(x) = u'v + uv' u = 7e 2x u' = 14e 2x v = sin(3x) v' = 3cos(3x) f'(x) = 14e 2x sin(3x) + 7e 2x 3cos(3x) f'(x) = 7e 2x ( 2 sin (3x) + 3 cos (3x) )
CK
Answered by Chris K. • Maths tutor
4454 Views