(a) y = Vr² – 25 (b) y = x+ /I| (Recall that |¤| = , ¤ > 0 ,* < 0*

Q: (a) Show that y for the given z = e" In x+ xy

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Q: Whch of the futowing tunction is a iner tunctiont Sx)- V3x -4 S(x) = x +5 O oton O outen f(x) = 2x…

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Q: 22 dt at x = 4. ind the linearization of f(x) = 7 - 4 +t

A: Consider the given function fx=7-∫7x+3224+tdt

Q: 19) * (xy)* = e ; f ind y' y' = [1+ In(xy)I y' = -y [1+ In Option 2 O Option 4 y' = [1- In(x None of…

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Q: If f(3) 12 and f '(x) 2 1 for 3 sxs 7, how small can f(7) possibly be? Enhanced Feedback

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Q: 1 Q9: Let f(x) = cosx x + 3 then find all critical points. 2 -

A: A critical number C is a number in the domain of 'f' for which eitherf'c=0 or f'cdoes not exists.…

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Q: Find L(x). 2y x 3t %3D y + a' = 3e-t x (0) = y (0) = 0 3s2 L (x) = - (s+1)(s-2)(s²+1) 3(s-1) L (x) =…

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Q: a)Evaluate y at position x=0.5  b)Evaluate the derivative dy/dx at position x=0.5. c)Using your…

A: For a given function of a single variable, its derivative represents at which rate the function is…

Q: Let y : R →R be the real-valued function defined on the real line, which is the solution of the…

A: Ans:-  Initial value problem: y'=-xy+x,  y=0=2          solution : y'+xy=x, 40=2          is of…

Q: الموضوع was althe eauation XÝY-2* Ý+4.=2* is a Linear differential Eauation and Heterogenious Dtrue…

A: The given statement

Q: 4 Find the linearization of the function f (x) = x² at x = 1. L(x) = Using this linearlization, ƒ…

A: f(x)=x4 at x=1 So, L(x)=f'(1)(x-1)+f(1)

Q: 2Use divectional devivative delinihion of f(Hiy)=x y'at the divecionof ū =i jatthe Point (le2>

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Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

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Q: Verify Young's Theorem y? x2 z = In(2x + y) – + e(x+2y) + - y

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Q: I. Use the limit of the rates as Ax approaches zero. Ar 1. y = Ax + B 2. y = 2x2 – 3x +5 3. y = x3

A: "Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 3. Suppose o1 and o2 are solution to y" + ay +by = f, where a and b are real constants and f is a…

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Q: x+2 32 dt at x = 4. 2+t 6 Find the linearization of f(x) = 3-

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Q: A ball is thrown upwards then falls back down to the ground. If h(t) represents the height of the…

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Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: [16.46° At 377 A=-0.25+ j7.9852 Stable -0.1693 -0.50

A: We will discuss how lambda is calculated. Lambda is the eigenvalues. I will show you how lambda is…

Q: 1 F(s) %3D 2 s+1 s+3 (s+2) 6 F(s) = e-s (s² +4).

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Q: 0. Suppose that x is the yield to maturity with continuous compounding on a zero-coupon bond that…

A: dB =[ (?B/?x) a(x0-x) + ?B/?t + ( 1/2) (?2B/?x2) s2x2] dt + (?B/?x)sxdz Since: B= e -x(T-t) The…

Q: What happens when you try to approximate V3 by using fixed point iteration of g(x) = 3/x?

A: To determine what happens when 3 is approximated using fixed-point iteration.

Q: Verify Young's Theorem In(2x + y) y2 x2 + + e(x+2y)

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Q: 2. Give an example of a regulated function f on [0, 1] such that f(x) > 0 for all æ e (0, 1), So…

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Q: ii. Establish the stability estimate for the solution of the problem "() - by(le) + ay(t) + f(4) on…

A: Given that , y''t=byt+ayt+fty''t=abyt+ft Therefore the differential equation , y''t-ab yt-ft=0 The…

Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: 1 Let H(s) Using convolution to find h(t) s2 (s-a)

A: Inverse Laplace transferom

Q: 2: The necessary condition for existence of the solution of the nonlinear equation x =g (x) in…

A: For any non linear function, to find the existence of its solution between an interval there should…

Q: 2y – x = 3t y+ x' = 3et 3e-t x (0) = y (0) = 0 3s2 L (x) = (s+1)(s–2)(s²+1) 3(2s3 –s–1) s2…

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Q: c) Solve the model for the detection of diabetes for critically damped case.

A: Given :The model for the detection of diabetes for critically damped case

Q: nake/s the DE nonlinear y' =1-xy+ y2

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Q: In an effort to make the distribution of income more nearly equal, the government of a country…

A: Given: Lorenz curve for first year: y = 0.97x2.1 And for the next year: y = 0.35x2 + 0.65.

Q: et Xi- Nco,1) and n=2 T=X,+Xz Show that Tis Sufficiencs y Statistic

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Q: Find the linearization L(x) of y = e3" ln(x) at a = 1. %3D L(x) = ||

A: See the details solution in the details solution

Q: SSS zdV Q3: Evaluate E + y² + z² = 1 and x² + y² + z² = 4 in the upper where E lies between the…

A: We have to evaluate the integral ∭EzdV, where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4…

Q: a'(t) = -x(t – 1), x(t) = 1 on [-1,0], is given by 1(t) = E(-1)* t – (k – 1))* k! for n-1<t <n, k=0

A: As per the question we are given the following first order time varient differential equation :…

Q: x+2 Find the linearization of f(x) = 6 - 21 dt at x=4. 1+t 6

A: Given a function f(x) at x=4 We have to find the linearization of f(x) at x=4 For solving this 1st…

Q: 1 4) S(x, y) = Ans. f(0,0) = -1 local max. x+y -1

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Q: B. Let z- ( x-y)e×y (x-y)exy Show: Zxx + zyy + exy Cya-x3)= -z (xy+ 2)

A: Partial derivative of a function z=f(x,y) with respect to x is the derivative of z keeping y…

Q: Let = f(x,y) = x² -y. Use Euler's method ( with step size h = 1) to approximate the value of y(2) if…

A: The Euler method is a first-order numerical procedure for solving ordinary differential equations…

Q: 2 3 4 5 ven the graph of f(x)above, determie the average rate of change of f(x) from x = 1 to x = 5.

A: we have to find

Q: 2. Evaluate f(x) = e3x + 2 at x = -1. Round to the nearest thousandth. %3D %3D f(-1) = ...

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Q: If f(x) > g(x) >0 for X in [1,0) and g(x) dx diverges to +0, then | F(x)dx also diverges to +. True…

A: It is TRUE, that 0&lt;g(x)≤f(x) for x in [1,∞)  and                               ∫1∞g(x)dx diverges…

Q: Find the linearization L(x) of y=e10xln(x) at a=1

A: y=e10xln(x)  The linearization L(x) of a function f(x) at x = a is, Now  Now differentiating given…

Q: Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

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Q: se Euler method to compute ys for the DE yy'=2 x for y(1)=3

A: Euler's Method