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One approach would be to use integration by parts, as we have two functions of x within the integral. This approach would get you to the answer but would be more difficult and convoluted than necessary. O...

Our DE (Differential Equation) dx/dt = 8sin(2t)/(3sqrt(x)) is separable because dx/dt can be expressed as a product of two functions of the form dx/dt = f(t)g(x) = (8sin(2t)) * (1/(3sqrt(x))).To solve the...

sin2x = 2sinxcosxcos2x = cos²x - sin²x=2 cos²x - 1= 1 - 2sin²xtan2x = (2tanx)/(1-tan²x)

The first thing when seeing such a question is to find out what the question wants you to do and plan your method to do so.In this case, the question asks you to find the normal of a curv...

First, if k=0 then the equation has no real roots since in this case we would have 5=0 (this is a proof by contradiction).
A quadratic equation of the form ax^2+bx+c=0 has no real roots if the discri...