University and College Calculus Solutions

CHECK THE LINK BELOW THIS HEADING FOR SOLUTIONS! Remember to check the corresponding Questions on the memo only Click here to view the solutions to the question below 2. (a) Sketch the straight line \(2x + 3y + 4\) (b) Find the equation of the straight line which is perpendicular to the line in (a) and goes through the point (1,1) (c) Sketch the two lines on the \(xy\)-plane 3. As dry air moves upward, it cools at a rate of about 1°C for each 100 m rises, up to about 12 km. (a) If the ground temperature is 20°C find a formula for the temperature (T) at height \(h\) (in km. (b) What range of temperature can be expected if a plane takes off and reaches a maximum height of 5 km. 6. Sketch the graph of \(y = |2x^2 - 3x - 2|\). 7. Sketch the graph of \(y = x^2 - 10x + 28\) by completing the square and applying some translations to the graph of \(y = x^2 \) 9. Given the functions: \(f(x) = 2x^2 = 2\) \(g(x) = \sqrt{x^2 - 4}\) Find the

CHECK THE LINK BELOW THIS HEADING FOR SOLUTIONS! Remember to check the corresponding Questions on the memo only Click here to view the solutions to the question below 5. If \(f(x) = 3x^2 - x + 2\), find: \(f(2), f(a), f(-a), f(a + 1), 2f(a), f(a^2), [f(a)]^2\) and \(f(a + h)\). 6. Evaluate the difference quotient for the given function. Simplify your answer. (a) \(f(x) = 4 + 3x - x^2, \frac{f(3 + h) - f(3)}{h}\) (b) \(f(x) = x^3, \frac{f(a + h) - f(a)}{h}\) (c) \(f(x) = \frac{1}{x}, \frac{f(x) - f(a)}{x - a}\) (d) \(f(x) = \frac{x+3}{x+1}, \frac{f(x) - f(1)}{x - 1}\) 7. Find the domain of the function (a) \(f(x) = \frac{x+4}{x^2-9}\) (b) \(f(x) = \frac{2x^3-5}{x^2+x -6}\) (c) \(f(x) = \sqrt[3]{2x - 1}\) (d) \(g(t) = \sqrt{3 - t} - \sqrt{2 - t}\) (e) \(h(x) = \frac{1}{\sqrt[4]{x^2-5x}}\) 8. Find the domain and the range and sketch the graph of the function \(h(x)=\sqrt{4 - x^2}\) 9. Find the domain and sketch the graph of the function