Find the derivative of f(x) = sqrtx. State the domain of f. Estimate t | Mathematics I 2074

Mathematics I207410 marksNumerical: derivative, domain, areaReview of derivative

Find the derivative of $f(x) = \sqrt{x}$ . State the domain of $f$ . Estimate the area between the curve and the line $x = 0$ and $x = 2$ where curve is $y^2 = x$ . [3+2+5]

Find the derivative of $f(x) = \sqrt{x}$. State the domain of $f$. Estimate the area between the curve and the line $x = 0$ and $x = 2$ where curve is $y^2 = x$. [3+2+5]

Function: $f(x) = \sqrt{x}$ - Curve: $y^2 = x$ - Bounds: $x = 0$ and $x = 2$ - Marks split: [3 + 2 + 5] --- (a) Derivative of $f(x) = \sqrt{x}$ Using first principles: $f'(x) = \lim{h \to 0} \frac{\sqrt{x+h} - \sqrt{x}}{h}$ Multiply by the conjugate: $$= \lim{h \to 0} \frac{(\sqrt{x+h} - \sqr...

Function: $f(x) = \sqrt{x}$ - Curve: $y^2 = x$ - Bounds: $x = 0$ and $x = 2$ - Marks split: [3 + 2 + 5] --- (a) Derivative of $f(x) = \sqrt{x}$ Using first principles: $$f'(x) = \lim{h \to 0} \frac{\sqrt{x+h} - \sqrt{x}}{h}$$ Multiply by the conjugate: $$= \lim{h \to 0} \frac{(\sqrt{x+h} - \sqr...

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Find the derivative of f(x) = sqrtx. State the domain of f. Estimate the area between the curve and the line x = 0 and x = 2 where curve is y2 = x. [3+2+5]