posted by .

What is the limit of 1-2x^2 -2cosx + cos^2x all over x^2? please answer ASAP. TY

  • Math - trig?? -

    Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.

  • RSNHS -

    The limit as x approaches what? Goodness.

  • Calculus-Limits -

    There are different ways to approach this:
    1. Since both numerator and denominator evaluate to zero as x->0, l'Hôpital's rule applies.
    Differentiate the top with respect to x to get:
    and the bottom to get
    As x->0, both numerator and denominator still -> 0, thus we can apply again the rule, and differentiate:
    numerator: 2*sin(x)^2-2*cos(x)^2+2*cos(x)-4
    denominator: 2
    As x->0, the sin(x) term vanishes, and the cos(x) terms cancel out, resulting in -4 over 2 in the denominator.
    So the limit is -2.

    2. If you have done series expansions before, expand numerator into a power series, taking only terms up to x^4:
    Dividing by the denominator leaves us with
    and as x->0,
    -1152/576 = -2 as before.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus help again

    if f'(x)=cos x and g'(x)=1 for all x, and if f(0)=g(0)=0, then the limit x--->0 fo function f(x)/g(x)= okay, so f(x)=sinx g(x)=x and the f(0)=g(0)=0 is also satisfied and equals o. so the limit x-->o of sinx/x= is the answer …
  2. Trig

    prove the identity (sinX)^6 +(cosX)^6= 1 - 3(sinX)^2 (cosX)^2 sinX^6= sinx^2 ^3 = (1-cosX^2)^3 = (1-2CosX^2 + cos^4) (1-cosX^2) then multiply that out 1-2CosX^2 + cos^4 - cosX^2 + 2cos^4 -cos^6 add that on the left to the cos^6, and …
  3. Math - Solving for Trig Equations

    For the following equation, why cannot I not solve it?
  4. Math

    I've got quite a few problems. Please answer any of them in whole or in part. Thank you in advance. (For the record, you're not doing my homework; you're helping me understand it. These problems were not assigned.) (1). Determine the …
  5. RESPONSE to PreCalc Question

    h t t p : / / w w w . j i s k h a . c o m / d i s p l a y . c g i ?
  6. Math

    Explain how to do this with steps please. 1. Simplify cos(x-y)+cos(x+y)/cosx Formula: cosxcosy= cos(x+y)+cos(x-y)/2 cos(x-y)+cos(x+y)/cosx =cosxcosy/2cosx
  7. Math

    Explain how to do this with steps please. 1. Simplify cos(x-y)+cos(x+y)/cosx I did some of these so far, don't know if it is correct. Formula: cosxcosy= cos(x+y)+cos(x-y)/2 cos(x-y)+cos(x+y)/cosx =cosxcosy/2cosx
  8. Math

    Find the limit of (2cosx+3cosx-2)/(2cosx-1)as x tends to pi/3.
  9. Math, please help

    Which of the following are trigonometric identities?
  10. Trigonometry

    How do you simplify: (1/(sin^2x-cos^2x))-(2/cosx-sinx)?

More Similar Questions