a. On the same axes, sketch the curves of y = p(x) and y = q(x). p(x) = 4 − x² and q(x) = e^x.

b. State the number of positive roots and the number of negative roots of the equation x² + e^x − 4 = 0.

c. Show that the equation x² + e^x − 4 = 0 can be written in the form x = ±(4 − e^x)^1/2 The iterative formula

is used to find an approximate value for the negative root.

d. Calculate the values of x₁, x₂, x₃ and x₄ to 4 decimal places.

e. Explain why the starting value x₀ = 1.4 will not produce a valid result with this formula.

Transcribed Image Text:

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