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choose y in order that the Vectors a=7i+yj+k, b=3i+2j+k, c=5i+3j+k are linearly dependent.

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Prove that [a+b,b+c,c+a]=2[a b c]

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Gradient in orthogonal curvilinear coordinate system.

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Solve (D²+2)y = x²e³^x.

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Solution:-

L-Hopital rule.

L-Hopital rule states that when the limit of f(x)/g(x) is indeterminate(0/0 form) in that conditions the value of limit can be obtained by evaluating  the derivatives of  f(x) and g(x) i.e[f'(x)/g'(x)].