Question and Answers Forum

AllQuestion and Answers: Page 188

Question Number 201790 Answers: 1 Comments: 1

Question Number 201764 Answers: 1 Comments: 0

1. y = tgx − ctgx → y^′ = ? 2. y = (1 + x^2 ) arctgx → y^′ = ? 3. y = cos^4 x → y^′ = ? 4. { ((x = 2t)),((y = 3t^2 − 5t)) :} → x^′ , y^′ = ?

$$\mathrm{1}.\:\mathrm{y}\:=\:\mathrm{tgx}\:−\:\mathrm{ctgx}\:\:\rightarrow\:\:\mathrm{y}^{'} \:=\:? \\ $$$$\mathrm{2}.\:\mathrm{y}\:=\:\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{arctgx}\:\rightarrow\:\mathrm{y}^{'} \:=\:? \\ $$$$\mathrm{3}.\:\mathrm{y}\:=\:\mathrm{cos}^{\mathrm{4}} \:\mathrm{x}\:\rightarrow\:\mathrm{y}^{'} \:=\:? \\ $$$$\mathrm{4}.\:\begin{cases}{\mathrm{x}\:=\:\mathrm{2t}}\\{\mathrm{y}\:=\:\mathrm{3t}^{\mathrm{2}} \:−\:\mathrm{5t}}\end{cases}\:\:\:\rightarrow\:\:\:\mathrm{x}^{'} \:,\:\mathrm{y}^{'} \:=\:? \\ $$

Question Number 201763 Answers: 5 Comments: 0

Find: 1. ∫ cos3x cosx dx = ? 2. ∫ 3^x sinx dx = ? 3. ∫_(0 ) ^( 1) x e^(−x) dx = ? 4. ∫_1 ^( e) ln^2 x dx = ?

$$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\int\:\mathrm{cos3x}\:\mathrm{cosx}\:\mathrm{dx}\:=\:? \\ $$$$\mathrm{2}.\:\int\:\mathrm{3}^{\boldsymbol{\mathrm{x}}} \:\mathrm{sinx}\:\mathrm{dx}\:=\:? \\ $$$$\mathrm{3}.\:\int_{\mathrm{0}\:} ^{\:\mathrm{1}} \:\mathrm{x}\:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} \:\mathrm{dx}\:=\:? \\ $$$$\mathrm{4}.\:\int_{\mathrm{1}} ^{\:\boldsymbol{\mathrm{e}}} \:\mathrm{ln}^{\mathrm{2}} \:\mathrm{x}\:\mathrm{dx}\:=\:? \\ $$

Question Number 201762 Answers: 1 Comments: 0

Question Number 201956 Answers: 1 Comments: 1

Question Number 201727 Answers: 1 Comments: 0

∫_(π/6) ^(π/3) e^(sin x^(cos x^(tan x^(cot x^(sec x^(cosec x) ) ) ) ) ) dx

$$\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} {e}^{\mathrm{sin}\:{x}^{{c}\mathrm{os}\:{x}^{\mathrm{tan}\:{x}^{\mathrm{cot}\:{x}^{\mathrm{sec}\:{x}^{\mathrm{cosec}\:{x}} } } } } } {dx} \\ $$

Question Number 201729 Answers: 1 Comments: 10

The teacher can choose in 560 ways, provided that there are three students in each team. Knowing that five students do not want to participate, find the number of people willing to participate

Question Number 201724 Answers: 0 Comments: 0

lim_(x→0) ((e^x (x−2)+x+2)/x^3 ) solve it by not using taylor series or l′hopital rule.

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{{x}} \left({x}−\mathrm{2}\right)+{x}+\mathrm{2}}{{x}^{\mathrm{3}} }\:{solve}\:{it}\:{by}\:{not}\:{using} \\ $$$${taylor}\:{series}\:{or}\:{l}'{hopital}\:{rule}. \\ $$

Question Number 201722 Answers: 5 Comments: 1

Question Number 201715 Answers: 0 Comments: 0

Use Cauchy Riemann to verify whether f(z)=(1/(z(z+1))) is analytic.

$${Use}\:{Cauchy}\:{Riemann}\:{to}\:{verify}\:{whether}\: \\ $$$${f}\left({z}\right)=\frac{\mathrm{1}}{{z}\left({z}+\mathrm{1}\right)}\:{is}\:{analytic}. \\ $$

Question Number 201728 Answers: 1 Comments: 0

cos^2 4x ∙ sin^2 4x = 0,25 for equation [0;90] how many roots are there in the piece?

$$\mathrm{cos}^{\mathrm{2}} \:\mathrm{4x}\:\centerdot\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{4x}\:=\:\mathrm{0},\mathrm{25}\:\mathrm{for}\:\mathrm{equation} \\ $$$$\left[\mathrm{0};\mathrm{90}\right]\:\mathrm{how}\:\mathrm{many}\:\mathrm{roots}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{piece}? \\ $$

Question Number 201712 Answers: 0 Comments: 2

Question Number 201707 Answers: 1 Comments: 0

Question Number 201702 Answers: 1 Comments: 1

Find: ∫_1 ^( 3) dx ∫_x ^( x^3 ) (x − y) dy

$$\mathrm{Find}: \\ $$$$\int_{\mathrm{1}} ^{\:\mathrm{3}} \:\mathrm{dx}\:\int_{\boldsymbol{\mathrm{x}}} ^{\:\boldsymbol{\mathrm{x}}^{\mathrm{3}} } \:\left(\mathrm{x}\:−\:\mathrm{y}\right)\:\mathrm{dy} \\ $$

Question Number 201693 Answers: 3 Comments: 0

Question Number 201689 Answers: 1 Comments: 0

Question Number 201683 Answers: 0 Comments: 1

Starting from substituting z=x+iy. Identify the maximal region within which f(z) is analytic f(z)=(1/(z(z+1))). Note. Do not start by just differentiating f(z). Start by doing a substitution of x and iy and then verify Cauchy Rieman theorem.

$${Starting}\:{from}\:{substituting}\:{z}={x}+{iy}.\:{Identify} \\ $$$${the}\:{maximal}\:{region}\:{within}\:{which}\:{f}\left({z}\right)\:{is}\:{analytic} \\ $$$${f}\left({z}\right)=\frac{\mathrm{1}}{{z}\left({z}+\mathrm{1}\right)}.\: \\ $$$$ \\ $$$${Note}.\:{Do}\:{not}\:{start}\:{by}\:{just}\:{differentiating}\:{f}\left({z}\right).\: \\ $$$${Start}\:{by}\:\:{doing}\:{a}\:{substitution}\:{of}\:{x}\:{and}\:{iy}\:{and}\: \\ $$$${then}\:{verify}\:{Cauchy}\:{Rieman}\:{theorem}. \\ $$$$ \\ $$

Question Number 201681 Answers: 1 Comments: 0

f(x+1)−f(x)=3f(x)×f(x+1) D_f =N 2023×f(1402)=1 have equation f(x)=1 solution?

$${f}\left({x}+\mathrm{1}\right)−{f}\left({x}\right)=\mathrm{3}{f}\left({x}\right)×{f}\left({x}+\mathrm{1}\right) \\ $$$${D}_{{f}} ={N} \\ $$$$\mathrm{2023}×{f}\left(\mathrm{1402}\right)=\mathrm{1} \\ $$$${have}\:{equation}\:{f}\left({x}\right)=\mathrm{1}\:{solution}? \\ $$

Question Number 201680 Answers: 1 Comments: 0

⋐

$$\:\:\:\Subset \\ $$

Question Number 201679 Answers: 5 Comments: 0

Question Number 201660 Answers: 1 Comments: 0

An equilateral triangle inscribed in a parabola y^2 =4x. One of its vertices is at the vertex of the parabola. Find the length of each side of the triangle in units.

$${An}\:{equilateral}\:{triangle}\:{inscribed}\:{in}\:{a}\:{parabola} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{x}.\:{One}\:{of}\:{its}\:{vertices}\:{is}\:{at}\:{the}\:{vertex}\:{of}\:\:{the}\:{parabola}. \\ $$$${Find}\:{the}\:{length}\:{of}\:{each}\:{side}\:{of}\:{the}\:{triangle}\:{in}\:{units}. \\ $$

Question Number 201659 Answers: 2 Comments: 0

Find the shortest distance between point A(3,2) and curve y=(√x) (x>0).

$${Find}\:{the}\:{shortest}\:{distance}\:{between}\: \\ $$$${point}\:{A}\left(\mathrm{3},\mathrm{2}\right)\:{and}\:{curve}\:{y}=\sqrt{{x}}\:\left({x}>\mathrm{0}\right). \\ $$

Question Number 201654 Answers: 6 Comments: 0

Question Number 201653 Answers: 0 Comments: 0

Question Number 201646 Answers: 1 Comments: 0

Question Number 201644 Answers: 0 Comments: 0

Pg 183 Pg 184 Pg 185 Pg 186 Pg 187 Pg 188 Pg 189 Pg 190 Pg 191 Pg 192

Contact: info@tinkutara.com