Questions from General Calculus

Q: Use a table of values to estimate the value of the limit

Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.

Q: (a). By graphing the function f (x) =

(a). By graphing the function f (x) = (cos2x – cos x)/x2 and zooming in toward the point where the graph crosses the y-axis, estimate the value of limx→0 f (x). (b). Check your answer in part (a) by e...

Q: (a). Estimate the value of limx→0 = sinx

(a). Estimate the value of limx→0 = sinx/sinπx by graphing the function f (x) = (sin x)/(sinπx). State your answer correct to two decimal places. (b). Check your answer in part (a) by evaluating f (x)...

Q: (a). Estimate the value of the limit limx→0

(a). Estimate the value of the limit limx→0 (1 + x)1/x to five decimal places. Does this number look familiar? (b). Illustrate part (a) by graphing the function y = (1 + x)1/x.

Q: The slope of the tangent line to the graph of the exponential

The slope of the tangent line to the graph of the exponential function y = 2x at the point (0, 1) is limx→0 (2x – 1)/x. Estimate the slope to three decimal places.

Q: (a). Evaluate the function f (x) = x2

(a). Evaluate the function f (x) = x2 – (2x/100) for x = 1 1, 0.8, 0.6, 0.4, 0.2, 0.1, and 0.05, and guess the value of limx→0 (x2 – 2x/1000) (b). Evaluate f (x) for x = 0.04, 0.02, 0.01, 0.005, 0.00...

Q: The point P (1, ½) lies on the curve y

The point P (1, ½) lies on the curve y = x (1 + x). (a). If Q is the point (x, x/ (1 + x), use your calculator to find the slope of the secant line PQ correct to six decimal places) for the following...

Q: (a). If G (x) = 4x2 – x2

(a). If G (x) = 4x2 – x2, find G' (x) and use it to find equations of the tangent lines to the curve y = 4x2 – x3 at the points (2, 8) and (3, 9). (b). Illustrate part (a) by graphing the curve and th...

Q: Use continuity to evaluate the limit. limx→4 5

Use continuity to evaluate the limit. limx→4 5 + √x/√5 + x

Q: Locate the discontinuities of the function and illustrate by graphing.

Locate the discontinuities of the function and illustrate by graphing. y = ln (tan2x)