Questions from General Calculus


Q: Let f (x) = [[cos x]], -π

Let f (x) = [[cos x]], -π (a). Sketch the graph of (b). Evaluate each limit, if it exists. (c). For what values of a does limx→ a f (x) exist?

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Q: Use the Intermediate Value Theorem to show that there is a root

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. x4 + x - 3 = 0 (1, 2)

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Q: (a). Prove that the equation has at least one real

(a). Prove that the equation has at least one real root. (b). Use your calculator to find an interval of length 0.01 that contains a root. ln x = 3 – 2x

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Q: (a) Prove that the equation has at least one real

(a) Prove that the equation has at least one real root. (b) Use your graphing device to find the root correct to three decimal places. 100e-x/100 = 0.01x2

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Q: For the function whose graph is given, state the value of

For the function whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why.

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Q: (a) Prove that the equation has at least one real

(a) Prove that the equation has at least one real root. (b) Use your graphing device to find the root correct to three decimal places. √x - 5 = 1/x + 3

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Q: Is there a number a such that limx→2 3x2 +

Is there a number a such that limx→2 3x2 +ax + a+ 3/x2 + x - 2 exists? If so, find the value of a and the value of the limit.

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Q: Is there a number that is exactly 1 more than its cube

Is there a number that is exactly 1 more than its cube?

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Q: A Tibetan monk leaves the monastery at 7:00 AM and

A Tibetan monk leaves the monastery at 7:00 AM and takes his usual path to the top of the mountain, arriving at 7:00 PM. The following morning, he starts at 7:00 AM at the top and takes the same path...

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Q: Use the Intermediate Value Theorem to show that there is a root

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex = 3 – 2x, (0, 1)

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