1.) Find all values of x for which the line that is tangent to y = 3x - tanx is parallel to the line y - x = 2

2.) Find the value of the constant A so that y = Asin3t satisfies the equation d^2y/dt^2 + 2y = 4sin3t

3.) Suppose that f(x) is a peacewise function shown below, for what values of k is f?

f(x) = (x^2) - 1, x <(or equal to) 1

= k(x - 1), x > 1

a.) Is it continuous?

b.) Is it differentiable?

Any help would be very much appreciated. :)

Guest Mar 25, 2015

#1**+5 **

1.) Find all values of x for which the line that is tangent to y = 3x - tanx is parallel to the line y - x = 2

ALWAYS remember that when you differentiate you are finding the gradient to the tangent of a curve

$$\\y=3x-tanx\\

y'=3-sec^2x\\\\

y-x=2\\

y=x+2\\

y'=1\\\\

1=3-sec^2x\\

-2=-sec^2x\\

2=sec^2x\\

\frac{1}{2}=cos^2x\\

cos x = \pm\frac{1}{\sqrt2}\\

x= n\pi\pm \frac{\pi}{4}\qquad n\in Z$$

1.) Find all values of x for which the line that is tangent to y = 3x - tanx is parallel to the line y - x = 2 - See more at: http://web2.0calc.com/questions/stuck-on-calculus#sthash.cD8MZGpc.dpuf

Melody
Mar 25, 2015

#3**+5 **

2.) Find the value of the constant A so that y = Asin3t satisfies the equation d^2y/dt^2 + 2y = 4sin3t

I assume this is

d^{2}y/dt^{2} + 2y= 4sin3t

If y= Asin3t

dy/dt = 3Acos3t

And

d^{2}y/dt^{2 }= -9Asin3t

So

d^{2}y/dt^{2} + 2y= 4sin3t

-9Asin3t + 2(Asin3t) = 4sin3t

-7Asin3t = 4sin3t

A = -4/7

CPhill
Mar 25, 2015

#4**+5 **

**Chris** maybe I am going a little balmy but I think your correction is identical to my original answer.

They are presented differently but I think that they are the same.

Melody
Mar 25, 2015

#5**+5 **

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CPhill
Mar 25, 2015