8. x' + 10x² + 6x + 4 is concave down. 3 Determine the interval(s) at which f(x) = -- a) O(-1, 00) b) O (-00, 5) c) O (-0, -1), (5, ∞) d) O(-1, 5) e) O (-00, -5), (1, ∞)

Q: 4) Find linear ditterental equation with costnt y-ac'+cadk Lomageneas coetfients whose general…

A:

Q: Bounded by the curve y = (x + 3)², the x axis, and the lines x =-3 and x= 0. %3D

A:

Q: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: (a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of…

A:

Q: 2. Compute F-dr where E= (x+ y,x-2z,z- y) and curve C is the line segment from (-3,5,1) C to…

A: Using line segment as the base of a rectangle, we choose the height to be the height of the surface…

Q: 5. Deduce the standard linear approximation of 1 x2+y2+z2 at Po(1,2,3).

A: The general formula of the standard linear approximation for f(x,y,z) is generally given by,…

Q: The curve ax4+bx3+cx2+dx+k passes thru P1 (5, –210), has a critical point at P2 (4, –416), and an…

A: Given The curve ax4+bx3+cx2+dx+k passes through P15,-210, has a critical point at P24,-416 and an…

Q: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

A:

Q: Determine a,b,c and d so that the curve y=ax^3 + bx^2 + cx + d will have a critical point at (0,-2)…

A: we have to determine a,b,c and d so that the curve y=ax3+bx2+cx+d will have a  critical point at…

Q: 8) Find the family Coff esponding to of orthogonal trajectories y=kx".

A: To find the orthogonal trajectories corresponding to below curve.

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

A:

Q: Specifically a differential equations problem. Question in pic below. The first "Select" is either…

A: Here, f1(x)=ex+3 and f2(x)=ex-4

Q: x?y" – 4xy' + 6y = 0, y(-2) = 8, y'(-2) = 0

A:

Q: 4. Estimate the In (1.1) and sec (0.1) using a linear approximation and without using any kind of…

A:

Q: The first provider can provide at most 5 tons, and the second one at most 3 tons. Finally, in order…

A: (2): Given equation is x≥2y-1 Draw the diagram of domain P

Q: 19. Give the midpoint approximation of xdx with n = 2.

A: Here, to approximate the given integral ∫04x3dx  using midpoint approximation with n=2. Let, f(x)=x3…

Q: .8 Estimate the error if cos t is approximated by 1 2 in the 4! integral cost? -- + - dt.

A:

Q: What are the critical points of sin(x2-1), at the closed interval [-1,1]?

A: Given: The critical point is a funtion is the point where the derivative of the funtion is zero.…

Q: List the critical points of the function f(x, y) = (x − 1)³(y + 2)² for which the Second Partial…

A: Given fx,y=x-13y+22   To Find: The critical points of the above function for which the Second…

Q: 2- Max z =30 x, + 30 x2 X +2 x2 2 80, 3x +2x2 2 120, Simppler s.t. X, X, 20

A:

Q: 5. Use differentials to approximate V4 + In(1.2) correct to two (2) decimal places.

A: Let us take the function f(x)= √x f'(x)=1/(2√x) f(x+Δx)=f(x) + f'(x) . Δx   ___i) Here let us…

Q: Let C be the shortest path that connects t to ni and I = S. (coshz + 1)dz. Then I=0 1--sinh π+…

A:

Q: If (1,1) is a critical point of f(x,y) = x³ – 3x + 3y² – 6y then (1,1) is:

A: (1,1) is the local minimum point   explanation is given in below step

Q: Find both first partial derivatives. z = 4y²/x az ax az ду || ||

A: z=4y2x

Q: 2 35) Find a curve through the point (-4, 1) whose length integral, 1 s y s 2, is L = 1 +

A:

Q: 16. Let y = 4x² + 7x + 4. If Ax = 0.2 at x = 2, use linear approximation to estimate 4y Ay 2

A:

Q: 4. Find the first partial derivatives of the function. z= xsin(ry)

A: We will use the formula  (uv)'=uv'+u'v Given z=x sin(xy) Then the partial derivative with respect to…

Q: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

A:

Q: Use forward, backward and centered difference approximations to estimate the first derivate of: tx)…

A:

Q: Compute the partial derivative of h(x, z) = e4xz-3x²z. (Use symbolic notation and fractions where…

A: In this problem first we need to partially differentiate the function with respect to z and then put…

Q: 8. Use the fact that the critical points of f(x, y) are found when vf(x,y) = 0 to show that (-3,-2)…

A:

Q: 4 to Use the Trapezoidal Rule with n = 1 approximate J-1 V1-x³

A:

Q: If the curve y = ax^4 + bx^3 + cx^2 + dx + e pass through the point (-1, 8), be tangent to the line…

A: Definition used -           Equation of a tangent line -                         y-y1=f'(x1)(x-x1)…

Q: 4. You will need to use L'Hopitals Rule in this one Sxe-* dx

A: This is a improper integral problem

Q: 4 Find the distance between u = -3and z= - 1 8

A:

Q: Find the first partial deravatives of the function

A: Since, only question no. 21 is clearly visible in the image you have provided, that’s why we are…

Q: If Z = x + iy than Z is: Z = x - iy Z = -x + iy Option 3 Option 2 Z = x + iy Z = -x - iy Option 4…

A: Explanation of the answer is as follows

Q: Let C be the shortest path that connects 7 to ni and I = f. (coshz + 1)dz. Then --sinh π+ π(1- )…

A:

Q: What function should be used to minimize the distance between y = x + 5 and the point (3, 1)? O D(æ)…

A: Explanation of the solution is given below...

Q: -solve by exact (Differeneial Eauanian (8--メう)+ス dy tメ- Xy よx 二0

A: ''Since you have asked multiple questions in a single request, According to guidelines we will be…

Q: 9. The total cost and total avenue, in dollars, from producing x couches are given by C(x) = 1000(x²…

A:

Q: 6. Determine a, b, c and d so that the curve y = ax3 + bx2 + cx + d so that the curve will have a…

A: Note: Hi and thanks for your question! Unfortunately, as per our guideline, only one question should…

Q: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

A:

Q: Suppose ƒ is differentiable on (- ∞, ∞) andƒ(5.01) - ƒ(5) = 0.25. Use linear approximation to…

A: Given:        Suppose ƒ is differentiable on (−∞,∞) andf(5.01)−f(5)=0.25

Q: Suppose thát the share of total production consumed by player i is x / x+(n1)y, where is player i's…

A:

Q: 3. Find general Golution y" + y= Secx

A: Given that, find the general solution y''+y=sec3x (D2 +1)y=sec3x

Q: Let y = 5x² + 4x + 4. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay ~ Submit…

A:

Q: 5.If the tangent 1ine to the functlen fx)= axt-6x at X=- has the equatfon. y= 3x+2then 6=?

A:

Q: Once again, a particle travels at velocity t – 1 at time t. Divide the interval 0, 2 into 2k…

A: A particle travels at the velocity t-1 at time t.  We now divide the interval 0, 2 into 2k intervals…

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: