Test 2 solution - TEST 2 MATH 107 CALCULUS II(BIO Name...

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TEST 2 (04/19/2013, MATH 107, CALCULUS II (BIO))Name:Section:Score:In agreeing to take this exam, you are implicitly agreeing to act withfairness and honesty.Problems/Points1/102/203/104/205/206/20Scores1
2TEST 2 (04/19/2013, MATH 107, CALCULUS II (BIO))1.(10 points)Determine whether the following statements aretrue (T) or false (F) (You need not give an explanation). (Each oneis of 2 points)(a) If the partial derivatives∂f/∂xand∂f/∂yof a functionf(x, y)exist at a point (x0, y0), this function must be differentiable at(x0, y0).(b) Iff(x, y) is differentiable at (x0, y0), thenfis continuous at(x0, y0).(c) Suppose thatf(x, y) is a differentiable function. The gradientvector offat a point (x0, y0) is not perpendicular to the levelcurve through (x0, y0).(d) If (x0, y0) is a critical point off(x, y), thenfmust be differen-tiable at (x0, y0).(e) Iff(x, y) and its partial derivativesfx, fy, fxy, andfyxare con-tinuous on an open disk centered at the point (x0, y0), thenfxy(x0, y0) =fyx(x0, y0).Problems(a)(b)(c)(d)(e)T/FFTFFT
TEST 2 (04/19/2013, MATH 107, CALCULUS II (BIO))3

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