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AllQuestion and Answers: Page 332

Question Number 188234 Answers: 0 Comments: 0

Question Number 187804 Answers: 0 Comments: 0

Question Number 187790 Answers: 2 Comments: 0

Question Number 187789 Answers: 1 Comments: 0

Question Number 187780 Answers: 1 Comments: 0

solve ⌊ (1/(4 )) + 2^( x) ⌋ + ⌊ (1/2) + 2^( x+1) ⌋=1

$$ \\ $$$$\:\:{solve} \\ $$$$\:\:\:\:\lfloor\:\:\frac{\mathrm{1}}{\mathrm{4}\:}\:+\:\mathrm{2}^{\:{x}} \:\rfloor\:+\:\lfloor\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{2}^{\:{x}+\mathrm{1}} \:\rfloor=\mathrm{1} \\ $$$$ \\ $$

Question Number 187776 Answers: 2 Comments: 0

Question Number 187774 Answers: 2 Comments: 0

Question Number 187765 Answers: 3 Comments: 0

Question Number 187762 Answers: 0 Comments: 0

if point P is any point inside △ABC with side lenghts a,b and c. prove that; ((PA)/a) + ((PB)/b) + ((PC)/c) ≥ (√(3 ))

$$ \\ $$$$\:\:\:\:\:\:\boldsymbol{{if}}\:\boldsymbol{{point}}\:\boldsymbol{{P}}\:\:\boldsymbol{{is}}\:\boldsymbol{{any}}\:\boldsymbol{{point}}\:\boldsymbol{{inside}}\:\:\: \\ $$$$\:\:\:\:\:\:\:\bigtriangleup\boldsymbol{{ABC}}\:\:\boldsymbol{{with}}\:\boldsymbol{{side}}\:\boldsymbol{{lenghts}}\:\boldsymbol{{a}},\boldsymbol{{b}}\:\boldsymbol{{and}}\:\boldsymbol{{c}}.\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{{prove}}\:\boldsymbol{{that}}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\boldsymbol{{PA}}}{\boldsymbol{{a}}}\:+\:\frac{\boldsymbol{{PB}}}{\boldsymbol{{b}}}\:+\:\frac{\boldsymbol{{PC}}}{\boldsymbol{{c}}}\:\geqslant\:\sqrt{\mathrm{3}\:} \\ $$$$ \\ $$

Question Number 187760 Answers: 1 Comments: 2

Question Number 187754 Answers: 1 Comments: 0

Question Number 187752 Answers: 0 Comments: 5

Question Number 187759 Answers: 0 Comments: 0

Question Number 187731 Answers: 4 Comments: 0

Question Number 187730 Answers: 1 Comments: 0

Evaluate lim(x,y)→(0,0) ((x^2 (y−1)^2 )/(x^2 +(y−1)^2 ))

$$\:{Evaluate}\: \\ $$$${lim}\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)\:\frac{{x}^{\mathrm{2}} \left({y}−\mathrm{1}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} +\left({y}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 187729 Answers: 0 Comments: 0

Question Number 187721 Answers: 1 Comments: 0

Question Number 187716 Answers: 2 Comments: 0

Question Number 187714 Answers: 1 Comments: 2

Question Number 187713 Answers: 1 Comments: 1

Question Number 187706 Answers: 1 Comments: 0

Question Number 187711 Answers: 0 Comments: 0

Evaluate lim(x,y)→(1,0) ((xy−y)/(x^2 +y^2 −2x+1))

$$\:{Evaluate}\:\: \\ $$$$\:\:\:{lim}\left({x},{y}\right)\rightarrow\left(\mathrm{1},\mathrm{0}\right)\:\:\frac{{xy}−{y}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}} \\ $$

Question Number 187703 Answers: 2 Comments: 0

∫ (1/(5x^2 − 2x − 4)) dx

$$\int\:\frac{\mathrm{1}}{\mathrm{5x}^{\mathrm{2}} \:\:−\:\:\mathrm{2x}\:\:−\:\:\mathrm{4}}\:\mathrm{dx} \\ $$

Question Number 187701 Answers: 1 Comments: 0

Question Number 187700 Answers: 0 Comments: 1

Find minimum area of the part y=x^2 and y=kx(x^2 −k), k>0

$$\:{Find}\:{minimum}\:{area}\:{of}\:{the}\:{part} \\ $$$$\:{y}={x}^{\mathrm{2}} \:{and}\:{y}={kx}\left({x}^{\mathrm{2}} −{k}\right),\:{k}>\mathrm{0}\: \\ $$

Question Number 187695 Answers: 2 Comments: 0

If , f( x )= (( sin_ (cos (x) ))/( ^ (√( (π/x))))) ⇒ f ′ ((( π)/2) ) = ?

$$ \\ $$$$\:\:\:{If}\:,\:\:{f}\left(\:{x}\:\right)=\:\frac{\:\:{si}\underset{} {{n}}\:\left({cos}\:\left({x}\right)\:\right)}{\overset{} {\:}\sqrt{\:\frac{\pi}{{x}}}} \\ $$$$\:\:\:\:\Rightarrow\:\:\:{f}\:'\:\left(\frac{\:\pi}{\mathrm{2}}\:\right)\:=\:? \\ $$

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