Questions **Question 1:** If f(x) = x2 then find fracf(2+h)-f(2)h **Qu | Mathematics I 2077

Mathematics I207712.5 marksNumerical: Difference quotient and tangent lineLinear mathematical model

Questions

Question 1: If $f(x) = x^2$ then find $\frac{f(2+h)-f(2)}{h}$

Question 2: Dry air is moving upward. If the ground temperature is $20°C$ and the temperature at a height of $1$ km is $10°C$ , express the temperature $T$ in $°C$ as a function of the height $h$ (in kilometers), assuming that a linear model is appropriate.

(b) Draw the graph of the function in part (a). What does the slope represent?

Question 3: Find the equation of the tangent to the parabola $y = x^2 + x + 1$ at $(0, 1)$ . [2.5+5+5]

Questions

Question 1: If $f(x) = x^2$ then find $\frac{f(2+h)-f(2)}{h}$

Question 2: Dry air is moving upward. If the ground temperature is $20°C$ and the temperature at a height of $1$ km is $10°C$, express the temperature $T$ in $°C$ as a function of the height $h$ (in kilometers), assuming that a linear model is appropriate.

(b) Draw the graph of the function in part (a). What does the slope represent?

Question 3: Find the equation of the tangent to the parabola $y = x^2 + x + 1$ at $(0, 1)$. [2.5+5+5]

Part 1: $f(x) = x^2$ ; evaluate the difference quotient at $x = 2$ . Part 2: Dry air moving upward. - Ground level: $h = 0$ km, $T = 20^\circ C$ - Height: $h = 1$ km, $T = 10^\circ C$ - Linear model assumed. Part 3: Parabola $y = x^2 + x + 1$ ; tangent required at point $(0, 1)$ . --- (a) Difference ...

Part 1: $f(x) = x^2$; evaluate the difference quotient at $x = 2$. Part 2: Dry air moving upward. - Ground level: $h = 0$ km, $T = 20^\circ C$ - Height: $h = 1$ km, $T = 10^\circ C$ - Linear model assumed. Part 3: Parabola $y = x^2 + x + 1$; tangent required at point $(0, 1)$. --- (a) Difference ...

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