Questions from General Calculus


Q: What is the slope of the curve y = 1/(3x

What is the slope of the curve y = 1/(3x - 5) at x = 1? Write the equation of the line tangent to this curve at x = 1.

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Q: Find the equation of the tangent line to the curve y =

Find the equation of the tangent line to the curve y = x2 at the point (3/2 , 9/4). Sketch the graph of y = x2 and sketch the tangent line at (3/2, 9/4).

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Q: Find the equation of the tangent line to the curve y =

Find the equation of the tangent line to the curve y = x2 at the point (-2, 4). Sketch the graph of y = x2 and sketch the tangent line at (-2, 4).

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Q: Determine the equation of the tangent line to the curve y =

Determine the equation of the tangent line to the curve y = 3x3 - 5x2 + x + 3 at x = 1.

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Q: Determine the equation of the tangent line to the curve y =

Determine the equation of the tangent line to the curve y = (2x2 - 3x)3 at x = 2.

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Q: In Fig. 1, the straight line has slope -1

In Fig. 1, the straight line has slope -1 and is tangent to the graph of f (x). Find f (2) and f ‘(2). Figure 1:

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Q: In Fig. 2, the straight line is tangent to the

In Fig. 2, the straight line is tangent to the graph of f (x) = x3. Find the value of a. Figure 2:

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Q: A helicopter is rising at a rate of 32 feet per second

A helicopter is rising at a rate of 32 feet per second. At a height of 128 feet the pilot drops a pair of binoculars. After t seconds, the binoculars have height s(t) = -16t2 + 32t + 128 feet from the...

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Q: Each day the total output of a coal mine after t hours

Each day the total output of a coal mine after t hours of operation is approximately 40t + t2 – 1 /15 t3 tons, 0 ≤ t ≤ 12. What is the rate of output (in tons of coal per hour) at t = 5 hours?

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Q: Differentiate. y = x + 1 / (x

Differentiate. y = x + 1 / (x + 1)

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