lim Σf (xf) Δx)]. V Axi→.

Q: Find a if f(0) = 1, f(;) = }, f(1) = 2 and f(}) = f(}) = a give o f(x)dx = using the composite…

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

Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: Let y(t) be the solution of dy/dt = 0.3y(2 − y) with y(0) = 1. Determine limt→∞ y(t) without solving…

A:

Q: (b) lim (z.y)→(0,0) Vr4 + y3 +1–1

A: limit of the rational function

Q: Find the linearization L(x,y) of the function f(x,y) = x2 - 4xy + 5 at Po(5,4).

A:

Q: Vhich of the following is correct? A) dx = lim | 1 %3D xp- = lim 4 V.r+4 V.r+4 V.r+4 -2 V.x+4 B) S…

A:

Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits…

Q: Let y(t) be the solution of dy/dt= 0.3y(2 − y) with y(0) = 1. Determine lim t→∞y(t) without solving…

A:

Q: (a) i. Find Re{sec (x + iy)}.

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

Q: 2t dt = 1 – t4 lim x→1- A) B) 2 C) 0. D) 1. 1

A: Given limx→1-∫0x2t1-t4 dt

Q: t² + 1 t 1 %3D lim→1- h(t) = ?

A:

Q: Express in form y=f(x) by eleminating the parameter x = t , y = tan−1(t3 + et )

A: It is given that,

Q: For x = x(y + 3), y = y(x - 1), find the trace of the Jacobian at the fixed point x = 0, y* = 0.

A: Given system is x˙ =xy+3y˙ =yx-1 Fixed point :  x* =0, y*=0   Take   x˙ =fx, y,    y˙ =gx, y   then…

Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D

A:

Q: limx→o (t+1)f(t)dt Assume f (0) = 4 %3D 3x2

A: Explanation of the answer is as follows

Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

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Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

A:

Q: d?x +x = secy %3D dy2

A:

Q: Find fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

A:

Q: Find the d. c. of from definition. Vx

A: As per the question we have to find the derivative of the function : f(x) = 1/√x Using the limit…

Q: 1. a.) Use use the L’hospital rule lim(1+* dy b.) Use Devirative Rule to search dx from the equation…

A:

Q: 5x - 5y2 lim (z.y) (0,0) 7z+7y () Limit DNE 0. O 5/7 O 5/7

A:

Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

A:

Q: Without eliminating the parameter, find d²y at t = 2 1 x = 1

A:

Q: If y= Vx (x-1), find dy (Use rules, not a XP de finition

A:

Q: If y(t) solves the IVP dy = y2021 y2019 y(2021)= -2019, dt then lim y(t) is: t- 00 Oa. 1 O b. 00 O.O…

A: Given differential equation is dydt=y2021-y2019.       ........1 It is an autonomous differential…

Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

A: The given problem is to find the third degree taylor polynomial of given function f(x,y) about point…

Q: Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

A: Given problem:- Use Green's theorem to evaluate ∫c (xy + y2 )dx + x²dy  by the curve y = x and y =…

Q: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: lim, - „f(x) = 0, then fx)dx diverges Select one: O True False

A: The given statement is

Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

A:

Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: 2. Find dy where y = v3x3 +4x + 1.

A: Given y=3x3+4x+1

Q: b) Differentiate y = e (In3x) + tan (3y) with respect to x. %3D + 2e In 3x Ans: dy %3D 3 1-

A:

Q: O from the equation z = In(x² + y²) + Zyy Show that zxx %3D

A:

Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

A:

Q: dy If y = tan t , x = tan? t ,Find by using Chain Rule dx at t =

A: Let the two functions are xt and yt. The chain rule to find dydx is given by the following formula.…

Q: _Suppose w =+, x = cos² t, y = sin? t, z = ; dw Evaluate at t = 3, by using the Chain Rule dt

A:

Q: What is the I.F of dy/dx=(y+y^2)/x?

A:

Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

A:

Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

A:

Q: what is (x fyx+ fy) given fCKiy)= ey

A:

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx + x²dy by the curve y y = x2.

A:

Q: Si f(x) dx + 2f(t) + f(t) = 0, f(0) = 1. %3D Apply the Final Value Theorem to determine lim f (t).

A:

Q: Evaluate 2.xyz dx + x²zdy +x²ydz over the path r(t) = (t², sin(nt/4), e'“-2') for 0 <t<2.

A: The given integral is: I=∫C 2xyz dx+x2z dy+x2y dzOver the path:  r(t)=t2,  sinπt4,  et2-2t    for…

Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin xz; x = , y=t, z= t'

A:

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.