We read your photo as:

Given cosh x = 1/2(e^x + e^-x) and sinh x = 1/2(e^x - e^-x), Use these definitions to show cosh2 x - sinh2 x = 1, Show that cosh x + sinh x = e^x and simplify cosh x - sinh x.

Mathematics

ScanSolve AI Answer

Answer

0.28\text{0.28}

Step-by-step solution

4 steps

Here's how to solve question 5(a):

  1. Find the derivative of yy with respect to xx.

    Given y=3x2+2x−4y = 3x^2 + 2x - 4.

    dydx=ddx(3x2+2x−4)=6x+2\frac{dy}{dx} = \frac{d}{dx}(3x^2 + 2x - 4) = 6x + 2
  2. Determine the initial value of xx and the small change in xx.

    The initial value of xx is 2.
    The change in xx, denoted as Δx\Delta x, is the difference between the new value and the initial value:

    Δx=2.02−2=0.02\Delta x = 2.02 - 2 = 0.02
  3. Evaluate the derivative at the initial value of xx.

    Substitute x=2x = 2 into the derivative:

    dydx∣x=2=6(2)+2=12+2=14\frac{dy}{dx} \Big|_{x=2} = 6(2) + 2 = 12 + 2 = 14
  4. Calculate the small change in yy.

    The small change in yy, denoted as Δy\Delta y, is approximately given by Δy≈dydxΔx\Delta y \approx \frac{dy}{dx} \Delta x.

    Δy≈14×0.02=0.28\Delta y \approx 14 \times 0.02 = 0.28

    The small change in yy is 0.28\boxed{\text{0.28}}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp