Here is a plot of a vibrating string h: R2 R given by the C function...

      

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Here is a plot of a vibrating string h: R2 R given by the C function h(x, t) for several times t. h(x,t) 0:5 1 - + 1.5 h(x,5) h(x, 4) = h(x,6) h(x, 3) = h(x,7) h(x,2) = h(x,8) h(x, 1) h(x,9) x 2 (a) Determine whether each value is positive, negative, or zero. i) h(0.5,5) ii) h(1,3) (b) Determine whether each first order partial is positive, negative, or zero. ah i) (0.5,5) ah ii) (0.5,5) at h iii) (1,3) ah at iv) (1,3) (c) Determine whether each pure second order partial is positive, negative, or zero. ah i) 3x2 (0.5,5) a2h iii) x2 (1,3) ah ii) (0.5,5) at2 ah iv) atz (1,3) (d) Determine whether each mixed second order partial is positive, negative, or zero. ah i) (0.5,5) axat ah ii) -(0.5,5) tx ah ah iii) (1,3) iv) -(1,3) xt atax Here is a plot of a vibrating string h: R2 R given by the C function h(x, t) for several times t. h(x,t) 0:5 1 - + 1.5 h(x,5) h(x, 4) = h(x,6) h(x, 3) = h(x,7) h(x,2) = h(x,8) h(x, 1) h(x,9) x 2 (a) Determine whether each value is positive, negative, or zero. i) h(0.5,5) ii) h(1,3) (b) Determine whether each first order partial is positive, negative, or zero. ah i) (0.5,5) ah ii) (0.5,5) at h iii) (1,3) ah at iv) (1,3) (c) Determine whether each pure second order partial is positive, negative, or zero. ah i) 3x2 (0.5,5) a2h iii) x2 (1,3) ah ii) (0.5,5) at2 ah iv) atz (1,3) (d) Determine whether each mixed second order partial is positive, negative, or zero. ah i) (0.5,5) axat ah ii) -(0.5,5) tx ah ah iii) (1,3) iv) -(1,3) xt atax