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1. If f(x) is the function given by f(x) = e3x + 1, at what value of x is the slope of the tangent line to f(x) equal to 2?
2. dx =
3. The side of a square is increasing at a constant rate of 0.4 cm/sec. In terms of the perimeter, P, what is the rate of change of the area of the square, in cm2/sec?
4. If f is a vector-valued function defined by f(t) = (sin 2t, sin2 t), then f″(t) =
5. The height of a mass hanging from a spring at time t seconds, where t > 0, is given by h(t) = 12 - 4 cos(2t). In the first two seconds, how many times is the velocity of the mass equal to 0?
7. What is the trapezoidal approximation of ex dx using n = 4 subintervals?
8. Given x2y + x2 = y2 + 1, find at (1, 1).
9. If f(x) dx = a and f(x) dx = b, then f(x) dx =