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Chapter 1: Problem 8
Evaluate the following integrals. \(\int \frac{e^{x}+e^{-x}}{e^{x}-e^{-x}} d x\)
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Find the volume of the solid that results when the region bounded by \(x= \sqrt{5} y^{2}\) and the \(y\) -axis from \(y=-1\) to \(y=1\) is revolved around the \(y\) -axis.
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If \(\int_{30}^{100} f(x) d x=A\) and \(\int_{50}^{100} f(x) d x=B,\) then \(\int_{30}^{50} f(x) d x=\) (A) \(A+B\) (B) \(A-B\) (C) \(B-A\) (D) 20
The acceleration of a particle moving along the \(x\) -axis at time \(t\) is given by \(a(t)=4 t-12 .\) If the velocity is 10 when \(t=0\) and the position is 4 when \(t=0\) , then the particle is changing direction at (A) \(t=1\) (B) \(t=3\) (C) \(t=5\) (D) \(t=1\) and \(t=5\)
If \(f(x)=3 x^{2}-x,\) and \(g(x)=f^{-1}(x),\) then \(g^{\prime}(10)\) could be (A) 59 (B) \(\frac{1}{59}\) (C) \(\frac{1}{10}\) (D) \(\frac{1}{11}\)
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