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.

Here's how to solve question 5(a): Step 1: Find the derivative of y with respect to x. Given y = 3x^2 + 2x - 4. (dy)/(dx) = (d)/(dx)(3x^2 + 2x - 4) = 6x + 2 Step 2: Determine the initial value of x and the small change in x. The initial value of x is 2. The change in x, denoted as x, is the difference between the new value and the initial value: x = 2.02 - 2 = 0.02 Step 3: Evaluate the derivative at the initial value of x. Substitute x = 2 into the derivative: (dy)/(dx) |_x=2 = 6(2) + 2 = 12 + 2 = 14 Step 4: Calculate the small change in y. The small change in y, denoted as y, is approximately given by y ≈ (dy)/(dx) x. y ≈ 14 × 0.02 = 0.28 The small change in y is 0.28. Send me the next one 📸