O De fine fG) in a way that extends g8) = X -3 to be continuows at x=3

Q: Is) Phd an equetian f te tangerut lme et a point C0.0) on the cur ve X= t-144 Aswers: aj 2y-x>0…

A: Topic = Derivative

Q: The function f(z) =e² is: u(x.y)=e*cos(y) o u(x,y) =e*sin(y) ¤ contiuous in СО discontiuous in CO

A:

Q: Show that the function u e(xy) + Vry V(y/x) provides the quation = 0. dy?

A: Again differentiate,

Q: 1 Evaluate J JA (2²+v²)² dxdy, where A is determined by the conditions 1< x² + y? < 2.

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Q: Trouver les valeurs de m et n telles que la fonction f définie par 2(4-a2) si a 3 soit continue.

A: It is given that f(x) is continuous everywhere, so we can say that limit exists at the point x=2 and…

Q: Prove that flx)= (i+x)? + X and diverge Litx)? both

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Q: Numerically integrate f(x) = x2 from a=0 to b= 2 using a multiple segment (n-2) trapezoidal %3D…

A: Trapezoidal rule  ∫abf(x)dx≈Δx2​(f(x0​)+2f(x1​)+2f(x2)+2f(x3​)+⋯+2f(xn-1​)+f(xn​))whereΔx=b-an

Q: sume that f(t) is continuous on [a, b| and that u = g(t) is cont ferentiable on [a, b], then f(u)…

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

Q: T 2 If fo)= J* +?dt, use the fundemental theorem of culculus part 1, to find f'cx) fixs=

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Q: Calculate the trapezoid approximation of o xdx using four subintervals. O T5 = 21.52 O T5 - 23.25 T5…

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Q: Find the local linearization of f(z) =z² at 9. lo(z) = %3D

A: Given : f(x) = x2   x0 =  9

Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

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Q: Find the derivate of F(x): z con(2) V64 – t dt .

A: To find derivative of given function.

Q: E is the midpoint of FG DF = DG Given: Prove: DE I FG

A: From the data we have:

Q: Find the orthogonal trajectories of r= a sin? 0 where a be the arbitrary constant.

A: We have, r=a sin2θ .....................................................(1) Differentiating w.r.t.…

Q: Let H(x) integral ,for -2 ≤ x ≤2.Use geometry to evaluate H(2).

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Comi der Hhe falßlning. J= x' J = 6-x of the ragan bj intyng awea ef mgount to O Fnd the wi th ayact…

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Q: If foxJ= S** t'dt, use the fundemental theorem of culcolus, part 1, to find f'cx) fixs=

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Q: Find thequahen. perpenditar to i fine -個 epe at OD pr Find tha liit ultpy cen gale (ro a) Po FO…

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Q: Use the Cauchy-Riemann Equations to show that f(z) = z Im(z) is only differentiable at z =0 and find…

A: Cauchy-Riemann Equations: Let f=u+iv be a complex valued function , then the Cauchy-Riemann…

Q: e? The singular points of f (z) = that lies inside |z| are z(z²-1) 2 a. 1, –1 Ob. 0, –1 Ос. 0, 1 d.

A: We have to find the singular points of f(z) = ( ez / z(z2 - 1) ). that lies inside | z | = 1/2 are

Q: 3. Given f(x,y) = xy + y2 +1° ey Verify that fry = fyx %3D

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Q: se Usa Grean's Thaoram to ecaloate the boundary of the region (travarsad cantarclodase) acadrant…

A: Given data-                   ∫c( ex + y2)dx +( ey + x2)dy. Where, e = Boundary of the region. We…

Q: d?y taby = Fo cos ot, where wo, ware positive con- dt- stants, and Fo is an arbitrary constant. You…

A: Given differential equation, d2ydt2+ω02y=F0cosωt      ...(1)

Q: Show that (d/dz)ž does not exist anywhere, i.e., f (z) =z is non-analytic anywhere.

A:

Q: use the scond fundamental thearam Ot cal culus to find F'Cx) fex) = 3t dt 3.

A:

Q: a²f If f(x,y) = e" sin (r + y), then prove that дхду дудх %3D

A: Hi! You have posted two non-related subparts. As nothing is specified, we are answering only the…

Q: The function f(z) =e² is: O contiuous in C discontiuous in C Ou(x,y) =e*cos(y) Ou(x,y)=e*sin(y)

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Q: a/ tangent s lope rasinczo) ) when e zT 9. 父 A dy do 2 517 dる 2. fhe D not of tne above

A: Given,  r=sin (2θ) Recall:  Slope, m=dydx

Q: Evaluate the ff. DE. J'how your complete solutuon I t cas : aim x Csinix tsonx cas x -y)

A:

Q: For f(x, y) = cos(xy²), which of the followings is true? O fr = fy O fxy = fyx O frr = fyy O fryr =…

A: The given function is fx,y=cosxy2

Q: Calculate the trapezoid approximation of 5dx using four subintervals. O T5 = 0.60 O T5 = 0.40 O T5 =…

A: The trapezoid approximation of the given integral is given below.

Q: Show that h, G) = (x+ n) converges %3D x4り? pointwise fo fa)=1, VXE [I, ) ノ

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Q: Show that the function u = p(xy) + VrY v(y/x) provides the uation x2 = 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: Suppos analyts s? show work. you

A: Given that f is analytic. And z≤1 And f(0)=0 And f(5)≤5 The formula for derivative is,…

Q: EXERCISE 6. dy +y dr where A is an arbitrary constant () - (+*) + A, Given that prove that tan

A: Solve By substitution

Q: Thelem:-TP PTR har ociva bveof %eI,theu f is Coutivlalse- at Xo CTs thecouvese of thevem triue?why?

A: Questions from continuity and differentiability

Q: a Use parseval's identity to prove that dt TC (a² + )(b + ?) 2ab (a + b)

A:

Q: Consider / f(x)dx. The approximation of I using composite trapezoidal rule with 3 subintervals is…

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Q: %3D a) Find fyxyx for f(x,y) = In(xy) – cos (xy) at (1,t).

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Q: Fnd the differentnad dy of the functen, sh Cx)

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Q: Given that F) = (yet coso)+(ayé-xsing)5 is conservative on R? (a) Find Potential gGay) Por F. (b)…

A:

Q: Given the interval [a,b] that saitisFies the hypothesis of Rolle's Theorem For the Furnction f(x) =…

A:

Q: E). f(x, y) = sen?(r2 – 0²) + In(r0 + 0), r = Vx2 + y² 0 = arctan con -

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Q: Find f, for f(x, y) = | cos(r*) dt.

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Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy

Q: 3. Given the graph of x' vs x, sketch the direction field for x(t) that corresponds. dx dt

A: Use the graph to draw the direction field. Observe how the graph passes through the visible points…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.