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3 years ago

Find the value of the expression whenx=1, y=-1,z =0a)5y –y b) 3x² +2y + 3z² c) 2y² -3xyz

Mathematics

1 answer:

7nadin3 [17]3 years ago

4 0

Answer:

a) 4

b) 1

c)2

Step-by-step explanation:

a) 5y - y

= 5 - 1

b) 3×1×1 + 2×1 + 3×0×0

= 3 - 2 + 0

c) 2×1×1 - 3×1×1×0

= 2 - 0

= 2

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Answer:

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Step-by-step explanation:

The Derivative of a Function

The derivative of f, also known as the instantaneous rate of change, or the slope of the tangent line to the graph of f, can be computed by the definition formula

$\displaystyle f'(x)=\lim\limits_{\Delta x \rightarrow 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$

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If we set

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$\displaystyle u'=1+\frac{x}{\sqrt{1+x^2}}$

Taking the derivative of y

$y'=3[tan^{-1}(x+\sqrt{1+x^2})]'$

Using the change of variables

$\displaystyle y'=3[tan^{-1}u]'=3\frac{u'}{1+u^2}$

$\displaystyle y'=3\frac{u'}{1+u^2}=3\frac{1+\frac{x}{\sqrt{1+x^2}}}{1+(x+\sqrt{1+x^2})^2}$

Operating

$\displaystyle y'=3\frac{1+\frac{x}{\sqrt{1+x^2}}}{1+x^2+2x\sqrt{1+x^2}+1+x^2}$

$\boxed{\displaystyle y'=3\frac{1+\frac{x}{\sqrt{1+x^2}}}{2+2x^2+2x\sqrt{1+x^2}}}$

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