Questions from General Calculus

Q: Make a rough sketch of the graph of the function. Do

Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given in Figures 3 and 13 and, if necessary, the transformations of Section 1.3. Figures 3: Figures 13...

Q: (a). Find parametric equations for the ellipse x2/a2

(a). Find parametric equations for the ellipse x2/a2 + y2/b2 = 1. [Hint: Modify the equations of the circle in Example 2.] (b). Use these parametric equations to graph the ellipse when a = 3 and b = 1...

Q: (a). How is the logarithmic function y = logax defined

(a). How is the logarithmic function y = logax defined? (b). What is the domain of this function? (c). What is the range of this function? (d). Sketch the general shape of the graph of the function if...

Q: (a). What is the natural logarithm? (b

(a). What is the natural logarithm? (b). What is the common logarithm? (c). Sketch the graphs of the natural logarithm function and the natural exponential function with a common set of axes.

Q: Find the exact value of each expression. (a).

Find the exact value of each expression. (a). log5 125 (b). log3 (1/27)

Q: Find the exact value of each expression. (a).

Find the exact value of each expression. (a). ln (1/e) (b). log10 √10

Q: Derive Equations 1 for the case π/2 < θ <

Derive Equations 1 for the case π/2 < θ < π.

Q: Find the exact value of each expression. (a).

Find the exact value of each expression. (a). e-2ln 5 (b). ln (ln ee10)

Q: Express the given quantity as a single logarithm. ln 5

Express the given quantity as a single logarithm. ln 5 + 5 ln 3

Q: Starting with the graph of y = ex, write the equation

Starting with the graph of y = ex, write the equation of the graph that results from (a). shifting 2 units downward (b). shifting 2 units to the right (c). reflecting about the x-axis (d). reflecting...