prove that lim (2X+iy2)=D4i %3D

Q: Use Green's theorem to calculate §. -y² dx + xy dy where C is the vertex triangle (1,3), (4,0) and…

A: Consider the given integral. I=∮c-y2dx+xydy The green theorem is defined as, ∮cPdx+Qdy=∬R∂Q∂y−∂P∂x…

Q: use the > & delinit of the f unchions ho prove that i Lim J19-X 3

A: The epsilon-delta definition of the limit: Let f(x) be defined for all x≠a over an open interval…

Q: What is lim m→0 sin(m) m ?

A:

Q: п! 1. Find lim via a Riemann Integral.

A:

Q: Compute limx→∞ cos(x) / x   (Hint: Remember the squeeze theorem?)

A:

Q: 5. Find the area and centroidal distances of the curve that lies between he equations y%3D4-x^2 and…

A: The region bounded by curves y=4-x2andy=x+2 To find the area and centroidal distances.

Q: In (1 +) lim t1/2

A:

Q: Show that limx,y)-(-2,0) g(x, y) does not exist given that (x + 2)³y² (x + 2)6 + 3y4' 0, if (x, y) +…

A:

Q: Express the limit as an integral. * lim (5(x)2 - 2(x;)³)Ax over [0, 3] i = 1 dx

A:

Q: V5+s-V5 lim s→0 S

A: lims→ 05+s-5s=lims→ 01s+5+5Plug in the value s=0=10+5+5=125

Q: Find the integral.

A: Given,

Q: 1 1 lim xV1+x

A: limx→01x1+x-1x=limx→01-1+xx1+x

Q: Let Fexy=4 Find Lim FAt and Lim FEX) X->2* 2 Does l tM fe) exist? Why zis FM cON tin-noss at X=27…

A: Answer

Q: Use the Squeeze Theorem to show that lim a sin (1/r) = 0. Show all %3D work. 2.

A:

Q: 2 Prove that limx* cos== 4 = 0. %3D - x→0

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Q: function holomorphic in 2 except p in an open neighborhood of w, the

A: To prove, ∫Tf(z)dz=0

Q: za z = e

A:

Q: Prove that lim x → 0+ (√x [1 + sin2( 2π/x )]) = 0 (using the squeeze theorem)

A:

Q: hey you didnt state the assumptions of the model and the limintations as well

A: To state: Assumptions and limitations of an exponential model.

Q: 7. Show that the horizontal lines y = 1 and y = -1 are asymptotes of y = tanh a and y coth r. %3D…

A:

Q: Exercise 3: Use the squeeze theorem to prove lim0 sin(x-1) = 0

A: To prove:

Q: L'Haspital X-rileniz lim

A:

Q: 1. Prove that lim vx sin O using the Squeeze Theorem.

A: Using squeeze theorem,

Q: Find the arclength of y = 2x /2 on 1 < ¤ < 3 2x3/2 uostion

A: given that y=2x3/2. we need to find the arc length in the interval [1,3] the arc length formulae is…

Q: Txーt e lim 4x² 4,2 +4x

A: Given that limx→0 e2x-14x2+4x We have to find the limit using L-Hopital rule L-Hopital's rule: If…

Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

A:

Q: Find the limits. Enter "DNE" if the limit does not exist. lim cos (x.y)¬(0,0) x' – y' x² + y² 4x lim…

A: Find the limits : Given :            lim(x,y)→(0,0)cosx7-y7x2+y2               =  cos 0-00+0…

Q: What is the lim, 0+ sin(y) In(y)?

A: limy→ 0+sinylny=limy→ 0+lny1sinyBy L'Hopital's rule,=limy→ 0+1y-cotycscy=limy→…

Q: find the limit:  limx→∞ (ln x)^3 / x^2

A:

Q: Maximize xyz on the ellipsoid

A: See the details solution in below

Q: 3 (e) lim (1 x2

A:

Q: エ→2ー Prove that lim sin(1/x) does not exist. Lot II

A:

Q: Evaluate limt--&gt;0(tan 4t)/(t sec t) Without using L'Hospital's rule.

A: To calculate the required limit without using the indeterminate form

Q: Prove that lim vx sin (2) = 0 using the Squeeze Theorem. x-0+

A:

Q: 1 Find lim dt

A: The given data is: limx→∞1x∫1xdtt  To find the value of the limit.

Q: The infinity in the V6-ydy can be eliminated by applying lim V6-y dy O True False

A:

Q: 1. Tangent to the parabola z = x + 3y?, x = 1, at point (1,2, 13

A:

Q: lim zsin lim z*. lim sin 1

A:

Q: Could you use L'Hopital's rule to solve the following question in its current form: lim,0+ In(x+1) O…

A: We have one of the following form limx→af(x)g(x)=00 or  limx→af(x)g(x)=±∞±∞  In these cases we have…

Q: Find the families of characteristics of the PDE (1-x²)w„ - u,, = 0 in the elliptic and hyperbolic…

A: Pde

Q: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…

A:

Q: 2xy Show that lim does not (x,y)→(0,0) x² + y² exist.

A: The limit function is limx,y→0,02xyx2+y2

Q: (i) Prove that Lim Vent +1 1 1 + + + /2n²+n] ... V2n2+2

A: Given that, g(x)=limn→∞12n2+1+12n2+2+....+12n2+n from sandwich theoram we can say if f(x)≤g(x)≤h(x),…

Q: Use the Squeeze Theorem to show that lim x* cos () = cos = 0.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Compute limx→0 sin(x) − x / x^3

A: To find the limit, simplify the expression and then apply the limit to each term in the expression.…

Q: OFind the aquahon of the Hangent to the at point Lircle X2 +8Xt PCI,3)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: An open rectangle box with volume 2m2 has a square base .express the surface s of the box as a…

A: Please find hand written solution.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.