Questions from General Calculus

Q: Find an equation of the tangent line to the curve at the

Find an equation of the tangent line to the curve at the given point. y = x3 - 3x + 1, (2, 3)

Q: (a). Can the graph of y = f (x

(a). Can the graph of y = f (x) intersect a vertical asymptote? Can it intersect a horizontal asymptote? Illustrate by sketching graphs. (b). How many horizontal asymptotes can the graph of y = f (x)...

Q: Determine lim x→1- 1/x3 – 1 and

Determine lim x→1- 1/x3 – 1 and limit x→1+ 1/x3 – 1 (a). by evaluating f (x) = 1/ (x3 – 1) for values of that approach 1 from the left and from the right, (b). by reasoning as in Example 1, and (c)....

Q: Sketch the graph of an example of a function f that satisfies

Sketch the graph of an example of a function f that satisfies all of the given conditions.

Q: Find an equation of the tangent line to the curve at the

Find an equation of the tangent line to the curve at the given point. y = 2x + 1/x + 2, (1, 1)

Q: (a). Find the slope of the tangent to the curve

(a). Find the slope of the tangent to the curve y = 3 + 4x2 - 2x3 at the point where x = a. (b) Find equations of the tangent lines at the points (1, 5) and (2, 3). (c). Graph the curve and both tange...

Q: (a). Find the slope of the tangent to the curve

(a). Find the slope of the tangent to the curve y = 1/√x at the point where x = a. (b). Find equations of the tangent lines at the points (1, 1) and (4, ½). (c). Graph the curve and both tangents on a...

Q: Evaluate the limit, if it exists. lim x →

Evaluate the limit, if it exists. lim x → 5 x2 - 5x + 6/ x – 5

Q: Use the definition of continuity and the properties of limits to show

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.

Q: If a ball is thrown into the air with a velocity of

If a ball is thrown into the air with a velocity of 40 ft/s, its height (in feet) after t seconds is given by y = 40t – 16t2. Find the velocity when t = 2.