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let f(x)=1.013x^5 −5.262x^3 −0.01732x^2 +0.8389x −1.912. Evaluate f(2.279) by first calculating (2.279)^2 ,(2.279)^3 ,(2.279)^4 and(2.279)^5 using four−digit round arithmetic. hence,compute the absolute and relative errors.

$$\boldsymbol{{let}}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\mathrm{1}.\mathrm{013}\boldsymbol{{x}}^{\mathrm{5}} −\mathrm{5}.\mathrm{262}\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{0}.\mathrm{01732}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{0}.\mathrm{8389}\boldsymbol{{x}} \\ $$$$−\mathrm{1}.\mathrm{912}.\:\boldsymbol{{Evaluate}}\:\boldsymbol{{f}}\left(\mathrm{2}.\mathrm{279}\right)\:\boldsymbol{{by}}\:\boldsymbol{{first}}\:\boldsymbol{{calculating}} \\ $$$$\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{2}} ,\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{3}} ,\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{4}} \boldsymbol{{and}}\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{5}} \:\boldsymbol{{using}} \\ $$$$\boldsymbol{{four}}−\boldsymbol{{digit}}\:\boldsymbol{{round}}\:\boldsymbol{{arithmetic}}.\:\boldsymbol{{hence}},\boldsymbol{{compute}} \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{absolute}}\:\boldsymbol{{and}}\:\boldsymbol{{relative}}\:\boldsymbol{{errors}}. \\ $$

Question Number 222838 Answers: 2 Comments: 0

Prove:∫_0 ^(1/2) ((ln(2x))/( (√(1+x^2 ))))dx=−(π^2 /(20))

$$\:\:\mathrm{Prove}:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{2}{x}\right)}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx}=−\frac{\pi^{\mathrm{2}} }{\mathrm{20}} \\ $$

Question Number 222845 Answers: 0 Comments: 0

Evaluate; Σ_(k=0) ^n (−1)^k (((2n − k)),(( k)) )

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Evaluate}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\:\left(−\mathrm{1}\right)^{{k}} \:\begin{pmatrix}{\mathrm{2}{n}\:−\:{k}}\\{\:\:\:\:\:\:\:\:{k}}\end{pmatrix} \\ $$$$ \\ $$

Question Number 222835 Answers: 0 Comments: 0

Question Number 222830 Answers: 1 Comments: 0

Question Number 222829 Answers: 1 Comments: 0

If f(x) = ((3x + [x])/(2x)) Find lim_(x→−5^+ ) f(x) − lim_(x→−5^− ) f(x) = ?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{3x}\:+\:\left[\mathrm{x}\right]}{\mathrm{2x}} \\ $$$$\mathrm{Find}\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow−\mathrm{5}^{+} } {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:−\:\underset{\boldsymbol{\mathrm{x}}\rightarrow−\mathrm{5}^{−} } {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$

Question Number 222828 Answers: 1 Comments: 0

vector field F^→ ;R^3 →R^3 , F_h ∈C^ω and Let′s define as A^→ =▽^→ ×F^→ can we find vector field F^→ .....??? Curl and Divergence inverse operator dose exist?? (▽_ ^→ ×)^(−1) A^→ , (▽_ ^→ ∗)^(−1) A^→ ex. ( ((d )/dx))^(−1) =∫

$$\mathrm{vector}\:\mathrm{field}\:\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}};\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}^{\mathrm{3}} \:,\:{F}_{{h}} \in\mathcal{C}^{\omega} \\ $$$$\mathrm{and}\:\mathrm{Let}'\mathrm{s}\:\mathrm{define}\:\mathrm{as}\:\overset{\rightarrow} {\boldsymbol{\mathrm{A}}}=\overset{\rightarrow} {\bigtriangledown}×\overset{\rightarrow} {\boldsymbol{\mathrm{F}}} \\ $$$$\mathrm{can}\:\mathrm{we}\:\mathrm{find}\:\mathrm{vector}\:\mathrm{field}\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}.....??? \\ $$$$\mathrm{Curl}\:\mathrm{and}\:\mathrm{Divergence}\:\:\mathrm{inverse}\:\mathrm{operator}\:\mathrm{dose}\:\mathrm{exist}?? \\ $$$$\left(\overset{\rightarrow} {\bigtriangledown}_{\:} ×\right)^{−\mathrm{1}} \overset{\rightarrow} {\boldsymbol{\mathrm{A}}}\:,\:\left(\overset{\rightarrow} {\bigtriangledown}_{\:} \ast\right)^{−\mathrm{1}} \overset{\rightarrow} {\boldsymbol{\mathrm{A}}} \\ $$$$\mathrm{ex}.\:\left(\:\frac{\mathrm{d}\:\:\:}{\mathrm{d}{x}}\right)^{−\mathrm{1}} =\int\: \\ $$

Question Number 222812 Answers: 1 Comments: 0