3. Determine if (х — 1)2, if x < 1 h(x) = %3D Vx – 1, if x > 1 is differentiable at x = 1.

Q: ölüm 5/ 11 - - Soru 5/11 Evaluate the following integral dx. (x² + 9)(x + 2) (Maksimum karakter…

A:

Q: If z = xe" and x = t2, y = Vt then the value of dz at t = 1 is equal to . dt Select one: True False

A: Solve the following

Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 9, find dt dy (а) If when x = 4. dt dy…

A:

Q: (i) Integrate the following functions with respect to x: 7 y =- 4x 2x - 3 y = 2 y = x* sin (x° +1)

A: Explanation of the answer is as follows

Q: Find dy and Ay for y = 3/x –1+ 2x at x = 2 with dr = Ar = 0.2.

A:

Q: and Suppose z is a function of a and y, and tan Vy2 + x² = z*e6y. Solve for dx dy

A:

Q: Given f(z) = | t2 – 16 dt 1+ cos²(t) OS At what value of a does the local max of f(x) occur?

A:

Q: Let dy/dx =f(x, y)= x^2 -y Use Euler’s method ( with step size ℎ = 1) to approximate the value of…

A: Given, dydx=f(x,y)=x2-y y(0)=1 h=1

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4. dy…

A:

Q: 10. Use differentials to estimate to estimate sin(46°). vZ(n+180) А. D. VZ(T+180) 360 180 В.…

A: Let y = sin (x)

Q: [2] Determine the values of n and h required to approximate | a In(x)dx to within 10-10. Use (a)…

A: Hello. Since your question has multiple parts, we will solve first question  for you. If you want…

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: dy for y= In(In(2r')) dt

A:

Q: Suppose that u and v are differentiable at x = 2 and that u(2) = 4, v(2) = -9, u'(2) = 5, and v'(2)…

A:

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

A:

Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 6, find dt dy when x = 4. dt (a) If dy…

A: Given y=2x+1 dydx=dydtdxdt

Q: If x =0.71 and y = 0.67, then value of C in the xsin-(x) V1-x² antiderivative of F(x) = is

A:

Q: Solve the following boundry-value problem by determining the appropriate Green's function via the…

A:

Q: 2 4 Q3) Evaluate the integral || xe" dy dx 0 x?

A: LetI=∫02∫x24xey2dydxchange the orderI=∫04∫0yxey2dxdyLet∫0yxey2dx=x∫0yey2dx∫0yxey2dx=ey2[x22]0y…

Q: ify+. 1 -dt = xy rsecx Q3.a) Find if y + S V sint+1

A: According to our answering guideline we can answer only first question if multiple questions are…

Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…

Q: -2 Evaluate the integral: ² ft² n s teu du ds dt

A:

Q: Suppose you know that dy/dt = 7y and that y(0) = 4. Which of the following answers is closest to…

A: We have to solve the differential equation

Q: Find the linear approximation of the given function at (0, 0). f(x,y) = sqrt(y+(cos(x))^2)

A: The given function fx, y=y+cos2x The linear approximation in 2 variables is given by Lx, y-fa,…

Q: Find the linear approximation of f(x) = In x at x = 1 and use it to estimate In(1.19). L(x) =…

A: Here f(x)=lnx at x=1We have to find the linear approximation of f(x) andAlso find the value…

Q: (b) If dy/dt = 2, find dx/dt when x = dx dt

A: By differentiating we solve the function

Q: Find the derivVative of the function. 5. y= In 8v +5 dy dv %3D

A: The objective is to find the derivative of the function.

Q: The tangent line to the curve y=f(x) is horizontal at where X = Xo f f(xx) = 00 A O f(xo) = 00 .8 O…

A: The tangent line to the curve y=f(x) is horizontal at where x=x0 if

Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

A:

Q: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

Q: Suppose y = V 2x + 1, where x and y are functions of t. %3D (a) If dx/dt = 9, find dy/dt when x = 4.…

A:

Q: Suppose y = V 2x + 1, where x and y are functions of t. (a) If dx/dt dy dt 15, find dy/dt when x =…

A:

Q: 14. Give the linear near-minimax approximation for f (x) = sin a on [–1, 1].

A: To determine linear near-minimax approximation for fx=sinx on -1,1 Let the approximation be px=a+bx…

Q: Find a positive value of k for which y=sin⁡(kt) satisfies d2y/dt2+16y=0.   k=

A: Double derivative

Q: For a. y′ =ln(y)+x,withy(1)=1. (Here x0 =1.) b. y′ =ln(1+y),withy(1)=0. (Here x0 =1.) Is it…

A: Solving for  a) y'=ln(y)+x            dydx=ln(y)+xdy=ln(y) dx+x dx Integrating:           ∫dy=∫ln(y)…

Q: 1) Find dy for each OF Following functions du a) y = cosh (2n) + 4 ny cosh (1an 2) + 2y = e * %3D F)…

A: Product rule of differentiation:   Chain rule of differentiation:

Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

A:

Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

A:

Q: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

A:

Q: Suppose y = (sq. root of) 2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt…

A: y=2x+1 Differentiating with respect to t, we get dydt=122x+1·d2x+1dt…

Q: 3 a) Find the exact integer value of a for which tsin (at)dt == ft sin (xt) dt = -². where a1. T

A:

Q: use euler's numerical method to obtain an approximation of y (0.6) with h = 0.1 where y(0.2)=1

A:

Q: Suppose y = /2x + 1 , where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4. (b)…

A: Differentiating with respect to t, we get

Q: use the integrating-factor method

A:

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt when x = 4. dy…

A: we will diferenciate the equation of y with respect to t, and solve this.

Q: 1. Defermine the integrating thators of the pallo wing non- exnet exact esuations. A. (1+ 4xy -…

A:

Q: Given Z = ye 3r + 2y; where a = ln 2 and y = 2 with possible errors Ax = 0.01 and Ay = 0.03.…

A:

Q: Q2) Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.