calculus

posted by .

Prove that there is a number that is exactly one more than its cube. (don’t solve just show there is one)

Prove that the function f(x)= cosx-x has a zero in (o. pi/2) Justify.

  • calculus -

    x = x^3 + 1
    x^3 - x + 1 = 0

    let f(x) = x^3 - x + 1

    every cubic function, just like every odd exponent equation, crosses the x-axis at least once.

    BTW, how about x = appr. -1.3247

    for cosx - x = 0
    cosx = x

    graph y = cosx an y = x on the same graph
    they only cross once, hence one solution

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-Calc

    Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= tanx + secx My work so far: (sinx/cosx + 1/cosx + cosx/cosx)/(sinx/cos x - 1/cosx + cosx/cosx)= tanx + cosx (just working on the left side) ((sinx + 1 - cosx)/cosx)/((sinx …
  2. Pre-calc

    prove the identity: (cosx)(tanx + sinx cotx)=sinx+cos(squared)x i need steps to show how i got the answer generally, it is a good idea to change all trig ratios to sines and cosines, and start with the more complicated-looking side. …
  3. Maths

    Please help with these questions: (please show how to do) 1. How many differently shaped rectangles, with positive integer dimensions, have a perimeter equal to their area?
  4. calculus

    prove that 5x - 7 - sin3x = 0 has at least one zero and prove that it has exactly one real zero. How am I supposed to show my work for this?
  5. Trignometry

    Can you please help me prove that ((1-cosx)/(1+cosx))=(cscx-cotx)^2?
  6. Precalculus/Trig

    Prove the following identity: 1/tanx + tanx = 1/sinxcosx I can't seem to prove it. This is my work, I must've made a mistake somewhere: Converted 1/tanx: 1/sinx/cosx + sinx/cosx = 1/sinxcosx Simplified 1/sinx/cosx: cosx/sinx + sinx/cosx …
  7. Math

    Find inverse of f if f(x)= x^2-4x+3, (for x is smaller than and equal to 2). First prove that f(x) is one to one in the defined domain of f and then obtain the inverse function. I know how to find the inverse. We just switch x and …
  8. Calculus

    1. Prove that (f(x+h)-f(x-h))/2=f'(x) 2. Prove that any parabola sastifies the equation (f(x+h)-f(x-h))/2=f'(x) For the first question, I tried to solve it but there is an extra h tacked on to one side. I have no clue what to do for …
  9. Calculus

    limit of (x*(y-1)^2*cosx)/(x^2+2(y-1)^2) as (x,y)->(0,1). By evaluating along different paths this limit often goes to 0. This does not necessarily imply that it exists. So how would i prove that it exists. Can someone please show …
  10. Mathematics

    mathematically, how to prove we cant divide by zero. and why multiplication of zero with any number leads to zero itself . can we mathematically prove that

More Similar Questions