Questions from General Calculus


Q: Graph the function f(x) = x3 + x2

Graph the function f(x) = x3 + x2 + x + 1 and explain why it is one-to-one. Then use a computer algebra system to find an explicit expression for f -1(x). (Your CAS will produce three possible expre...

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Q: a. If g(x) = x6 + x4,

a. If g(x) = x6 + x4, x ≥ 0, use a computer algebra system to find an expression for g-1(x). b. Use the expression in part (a) to graph y = t(x), y = x, and y = g-1(x) on the same screen.

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Q: If a bacteria population starts with 100 bacteria and doubles every three

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is n = f(t) = 100 ∙ 2t/3. a. Find the inverse of this function and explain...

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Q: When a camera flash goes off, the batteries immediately begin to

When a camera flash goes off, the batteries immediately begin to recharge the flash’s capacitor, which stores electric charge given by Q(t) = Q0(1 – e-t/a) (The maximum charge capacity is Q0 and t is...

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Q: Find the exact value of each expression. a. cos

Find the exact value of each expression. a. cos-1(-1) b. sin-1(0.5)

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Q: Find the exact value of each expression. a. tan

Find the exact value of each expression. a. tan-1 3 b. arctan(-1)

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Q: Find the exact value of each expression. a. csc

Find the exact value of each expression. a. csc-1 √2 b. arcsin 1

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Q: Find the exact value of each expression. a. sin

Find the exact value of each expression. a. sin-1(-1/√2 ) b. cos-1(√3/2)

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Q: Find the exact value of each expression. a. cot

Find the exact value of each expression. a. cot-1(-√3 ) b. sec-1

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Q: Evaluate the difference quotient for the given function. Simplify your answer

Evaluate the difference quotient for the given function. Simplify your answer.

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