# HS Calculus

posted by .

Help
Have some more that I do not understand.

Limit theta approaching zero
SinTheta minus Tan theta/ sin cubed theta

• HS Calculus -

Rewrite as [sin x(1 - 1/cosx)]/sin^3x
= [1 - (1/cosx)]/[1 - cos^2x]
Now use L'Hopital's rule and take the ratio of the derivatives of numerator and denominator. That lets you get rid of the 1's.
You are left with
Lim [-tanx secx/(2cosx sinx)]
= Lim -1/(2 cos^3x)
Which is -1/2

• HS Calculus -

It took me a while to get that one. I cheated and used a hand calculator first, and it agrees.

## Similar Questions

1. ### Maths- complex numbers

Find tan(3 theta) in terms of tan theta Use the formula tan (a + b) = (tan a + tan b)/[1 - tan a tan b) in two steps. First, let a = b = theta and get a formula for tan (2 theta). tan (2 theta) = 2 tan theta/[(1 - tan theta)^2] Then …
2. ### Calculus

Below are the 5 problems which I had trouble in. I can't seem to get the answer in the back of the book. Thanks for the help! lim (theta-pi/2)sec(theta) theta->pi/2 Answer: -1 I am not sure what to do here. lim (tan(theta))^(theta) …
3. ### HS Calculus

Have some more that I do not understand. Limit theta approaching zero SinTheta minus Tan theta/ sin cubed theta
4. ### HS Calculus

1) Limit theta approaching zero sin squared theta/ tan theta 2) Lim x appraoches zero x + sin x/x x + sin x/x = x/x + sinx/x 0 + 1 =1 My answer : 1 Is this correct
5. ### HS Calculus

1) Limit theta approaching zero sin squared theta/ tan theta 2) Lim x appraoches zero x + sin x/x x + sin x/x = x/x + sinx/x 0 + 1 =1 My answer : 1 Is this correct
6. ### Calculus

I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure …
7. ### math

I have a question I have been working on since yesterday and I am not making this up. I couldn't get the right answer. If sin theta = -2/3, which of the following are possible?
8. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …
9. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …
10. ### calculus

I have a definition lim theta approaching 0 sin theta/theta = 1 so show if the limit x approaching 0 sin2x/5=2/5

More Similar Questions