State the range of f (x) 1 3x+4 = 4 {y e R]y± - } O {y e R|y>0 } 4 {y e R|y> O {y e R|y#0 }

Q: Find all values of x such that dy/ldx = 0 where y is the function stated below. x2 y = -3x + 4)

A:

Q: Compare the values of delta y and dy for the function f(x)= x^3 - 3 at x=3and delta x= 0.2

A:

Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

A:

Q: 2x :S dr f(x, y) dy. f (x, y) dy. •1-x² f (x, y) dy. -V1-r

A:

Q: Minimize f(x) = x² + 54 ; using Interval halving method for 2 ≤ x ≤ 6. E= 10-³

A:

Q: The critical point of the function* f(x, y) = x² + 5y² + 2 cos x

A:

Q: of of and dy 6. For the function f(x.y) = sin ° (6x - 5y), find of df dy II

A: In partial derivative when take the derivative with respect to one variable consider other variables…

Q: Find the local linear approximation to f(x) = Vx at x = 1 and use it to approximate both 1.1 and…

A: To know which one is better we have to compare with calculator values of sqrt(1.1)  and sqrt(0.1)

Q: Suppose F(r, y) is a C' function such that F(0, 0) = 0. What conditions on F will guarantee that the…

A: Let us consider, F^(x,y)=F(F(x,y),y)  On applying the implicit function theorem , can get a solution…

Q: Q4/ 1- Evaluate: f/2fy sinx dy dx ди 2- If u = x² + ey² ,x= sin 2t , y = cost² find at

A:

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

A:

Q: find the absolute extrema of thefunction on the closed interval y=x \ln (x+3),[0,3]

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: Find the local maximum and minimum values and saddle point(s) of the function. (DNE if doesn't…

A:

Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

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: What is the linear approximation of the function f (x) = e x at x = 1?

A:

Q: A) Find and classify the critical points of f(z, y) = x³ + y3 – 6y? – 3.x + 9 using the first and…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: 10. The line y = 5x – 5 is tangent to the graph of f (x) = (x + k)(x² – x) at the point where x = 1.…

A:

Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: find the solution of following derivative by Runge-Kutta method f(x,y) = -2x3+ 12x2 - 20x + 8.5 let…

A: Consider an initial value problem dydx=f(x,y) with the initial condition yx0=y0. Then Runge-Kutta…

Q: What is local linear approximation for f(x)= e*" -6* near x = 0? Note: Must show answer is equal to…

A: Hey, since there are multiple subpart posted, we will answer the first question. If you want any…

Q: 3.Find the linear approximation to f(x) = cos x at x, = ÷ and use the linear approximation to…

A: We will use formula for linear approximation.

Q: find the general solution of dy/dx + (3/x)y=2/x^2 as a function of x

A: Given,           dydx+3xy=2x2

Q: If sin(x) f(x)= V2+t2 dt tan(x) and g(y)= f(x) dx g" (4) Then is equal to V5 - 2 V3 - 2V3 11 E- 2V3…

A: Given:            f(x)=∫tanxsinx2+t2dt  and g(y)=∫1yf(x)dx

Q: 8. Find a continuous solution satisfying dy dr + 2xy = f(x) where = x if 0 < x < 1 0 if x ≥ 1 off…

A: Solve the following

Q: A particle moves along the x-axis so that it’s position at any time t≥0 is given by…

A:

Q: (a) f(x) = e" centered at r = 0.

A:

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) L(x) =

A:

Q: Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

A:

Q: Find the extreme values of the function f (x, y) = e¬¤y given that (x, y) must live in the region…

A:

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

A:

Q: If y = x(x – 1)* then y' at z = 2 is equal to

A:

Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

Q: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

A:

Q: Suppose that f(0) = 1, ƒ(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…

A:

Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

A:

Q: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: 4. What is the maximum possible error if T4 is used to approximate | f(x) dx f(x) dx

A:

Q: The limit of f (x, y) : as (x,y) approaches (0,0): %3D O Infinity O Doesn't exist Exists and equal…

A:

Q: Find f fy. - f(x.y.z) = x - Vy² + 22? + 2z² = (Type an exact answer using

A: Here we have to find fx , fy and fz  of

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = sin(x), a = 2…

A:

Q: b) Find of the functions: dx 1: f(x)= tan (2x)Vī – 3x² %3D 10 2: x tan y + y" sec x 2x 3: y= csch'…

A:

Q: Calculate the error of approximation E, for: f(x) = v3x + when x = 8. Ax = dx = 0.1

A:

Q: 9. If f(x,y) = -cos x+e*y, find Vf(x, y).

A: For the solution follow the next step.