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 = x + c0s x, (0, 1)

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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 = 1/sin x + cos x, (0, 1)

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Q: (a). Find an equation of the tangent line to the

(a). Find an equation of the tangent line to the curve y = 2x sin x at the point (π/2, π). (b). Illustrate part (a) by graphing the curve and the tangent line on the same screen.

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Q: (a). Find an equation of the tangent line to the

(a). Find an equation of the tangent line to the curve y = 3x + 6 cos x at the point (π/3, π + 3). (b). Illustrate part (a) by graphing the curve and the tangent line on the same screen.

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Q: (a). If f (x) = sec x -

(a). If f (x) = sec x - x, find f'(x). (b). Check to see that your answer to part (a) is reasonable by graphing both f and f' for |x| < π/2.

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Q: (a). If f (x) = ex cos x

(a). If f (x) = ex cos x, find f'(x) and f"(x). (b). Check to see that your answers to part (a) are reasonable by graphing f, f', and f".

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Q: Trace or copy the graph of the given function f. (

Trace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it.

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Q: If f (t) = csc t, find f"(

If f (t) = csc t, find f"(π/6).

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Q: (a). Use the Quotient Rule to differentiate the function f

(a). Use the Quotient Rule to differentiate the function f (x) = tan x- 1/sec x (b). Simplify the expression for f (x) by writing it in terms of sin x and cos x, and then find f'(x). (c). Show that yo...

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Q: Differentiate. f (x) = sinx + 1/

Differentiate. f (x) = sinx + 1/2 cot x

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