13. (a) Estimate the value of lim- X x+√1+3x-1 X √1+3x-1 By graphing the function f(x) = - (b) Make a table of values of f(x) for x close 0 and guess the value of the limit. (c) Use the limit laws to prove that your guess is correct.

Q: ) Show that F = (2xy +2³) i+x²j+3r2²k is conservative force field. Find the scalar potential of F.

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Solve y" - 2y + y = 12e³t y(0) = -1 y'(0) = 0

A:

Q: (3-zi) (x+y)=3+2i +ゾー

A:

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A:

Q: 5. Determine whether the series converges or diverges. b. Σ... (1+2n)" a ΤΟ n=1

A:

Q: Find the area of the surface formed by revolving the ellipse about the z-axis (an ellipsoid) y² + a²…

A:

Q: Given the function C'(r) = (r − 1)( − 5r + 3)³(r − 2)5, - its roots are and their multiplicities are

A:

Q: Show that if s(3) 4(q- _9−2+9(1+ 93 2(g-1) increasing or decreasing. For 3 > 0, q> 3

A: The given function is                               sβ=q-2+q1+4q-1qβ122q-1 where β>0 and q>3.…

Q: Solve the initial value problem y(t) = c₁cost + c₂sint y(t) = = 8cost - 16sint y″ + y = 0, y(7) = 8,…

A:

Q: The response sensitivity of a toxic gas detection sensor is optimized based on two significant…

A: Let us solve the given problem in the next steps.

Q: (2x + y - 3z = -9 | x + 5z = 14 | −3x + 2y - z = 4). From 3 (three) equations, what is the value of…

A: Solution :-

Q: Task 2: Linear Programming Imagine you are trying to maximize the calories you burn in a 60-minute…

A: You didn't provide data in task 3  So here is you answer for task 2

Q: Let C be the code given by the matrix 0 1 1 Suppose x = (11010) and y = (10110)t are received.…

A: If G is a matrix, it generates the codewords of a linear code C by {\displaystyle w=sG} where w is…

Q: Goup 2. Tell if true or false the following statement, justifying carefully your response trough a…

A: The given statement is  " If 0 is the only eigenvalue of A then A is a zero matrix " In the next…

Q: дгу ду дх2 5- · + 4y = 0 дх In

A: Given differential equation is y''−5y'+4y=0.....1. We have to find the solution of the expression…

Q: 6. Given the demand equation, P = 100-Q, calculate the price elasticity of demand when P=3 $(a+ß).

A:

Q: Lucia checked her online bank statement which shows the current balance is $381.23, pending…

A:

Q: 3. p(x) = −(x − 1)(x + 1)(x + 2022) the characteristic polynomial of 1 € M3x3(C). Then: a) A is…

A:

Q: (2η)! (n!)². 2n 8. Σ(-1)n-1. n=1

A:

Q: Answer the following questions for the function defined on the interval [-5, 7]. a.) f(x) is concave…

A: From the above details we have,

Q: Solve: си ch= -|P I/2 (1) 2012/0 dt

A:

Q: Let X and Y be normed spaces. For F € BL(X,Y), define ||F|| = sup{||F(x)|| : x € X, ||1|| ≤ 1}. Then…

A: There are definitions of norms on bounded linear operators, they all are equivalent.

Q: n open field is bounded by a lake with a straight shoreline. A rectangular enclosure is to be…

A: This is the problem of the Application of Calculus.

Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y= 11e²x, y(0) = 1, y'(0) = 1 2x 7e -7.x…

A:

Q: Water freezes at 0 Celsius and 32 Fahrenheit. Water boils at 100 Celsius and 212 Fahrenheit. Write…

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

Q: S=S(x)=9/2+10+x/4, x>=4, Find limx->4^+S(x), Find limx->10 S(x)

A: Limit of the function

Q: 4. (a) Show that F (2xy + z³)i+x²j+3xz²k is conservative force field. Find the scalar potential of…

A: Please see the attachment

Q: = Use spectral decomposition to orthogonally diagonalize the matrix A [] -7 24 7 24

A:

Q: $ D Surface Aren So Sex & trift-gin 1-1/² D S= (6²-y²) =7 y b₂ SERS() JH (fa) dx 6² D 0 $10k Tave…

A: From the above details we have,

Q: 1-2 √1–7² √1-2 dz dr de rdz dr de dz dr de

A: Option d is correct answer

Q: Solve y" - 2y + y = 12e³t y(0) = -1 y'(0) = 0

A:

Q: find the number of the isomorphism classes of graphs with 5 vertices and 6 edges which have (i)…

A: Given the a graphs with 5 vertices and 6 edges. We have to find the number of the isomorphism…

Q: Let A be an nxn matrix with real entries, and let λ be an eigenvalue of. Which of the following…

A: It is given that A be an n×n matrix with real entries and λ be an eigen value of A. Then we have to…

Q: use bisection method not quadratic formula

A:

Q: please answer

A:

Q: Question 3: Use Lagrange Multipliers to find the absolute maximum value and absolute minimum value…

A:

Q: defined on the interval (-5,7). a.) f(x) is concave down on the open interval (-5,0) J(x)=xVx² +1…

A: From the above details we have,

Q: Solve the given initial-value problem. y(x): = y" + 6y' - 7y = 11e2x, y(0) = 1, y'(0) = 1 -7.x 2x 7e…

A:

Q: espect to some norm on X, but discontinuous with respect to another orm on X. To illustrate this,…

A:

Q: Answer all Questions Apply Newton-Raphson method to find an approximate solution of equation e-3 = 0…

A: We need to find the solution of the equation ex-3x=0 using Newton-Raphson method f(x)=ex-3x,…

Q: Q 11: Determine the measure of the central angle that is formed by and arc length of 5 cm in a…

A: Solution: Given, Arc length(s) = 5 cm            Radius(r) = 2.5 cm Now, We know that arc length(s)…

Q: find an equation of the surface of revolution generated by revolving curve equation of curve…

A:

Q: The weather in Columbus is either good, indifferent or bad on any given day. If the weather is good…

A: Given that: If the weather is good today, there is a 60⁒ chance the weather will be good tomorrow, a…

Q: 대 ㅎ I/2 (1) ju 27808 42 To dt

A:

Q: 10.2 Jo +8 1 + x3 dx

A: Follow the steps.

Q: In your own words define and provide an example of each of the three different isometric…

A: What is Isometric Transformation Isometric transformation is a major transformation in geometry. It…

Q: Suppose a, b ∈ R and a < b. Prove that a and b cannot be both roots of the equation x^3 + 5x = 4 cos…

A:

Q: . Using Green's theorem, show that the area of a plane region in polar coordinate is 1 $ C r²do.…

A:

Q: arctan(x) = x + lerror] < 0.0005

A: Given,        tan-1(x)=x-x33+x55  (error&lt;0.0005

Q: The spread of a fungal infection in an ant colony can be modeled by 2 where t is the time in hours…

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