2x - 6 Let f(x) = if x < 5 if x > 5 -4x+ 20 Find the following limits: 1. lim f(x) = x-5 2. lim f(x) = x-0 Type dne if the limit does not exist.

Q: 7. (10 pts) Evaluate the integral Sa x4 6x5 - 1dx

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Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density…

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Q: Q4) Find the maximum eigen value for the system 4 = x¹ (0) = (1 1) 3 12 54 with initial vector

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Q: Evaluate the following integrals: 4x 6. ²x3x²y²dy dx -TT/3 7. p² sin 0 de dp Jπ/6 S3

A: The integration of the integral is  6) 3x2y2 7) (row) 2sin(theta).

Q: 5. Solve the equation = 170. 6. Solve the following logarithmic equations. (a) log, (+5) = log, 3…

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Q: gh (2,-5), parallel to y= 2x+4

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Q: The equation of a hyperbola given below when reduced to standard form is 16y² -9x² +36x +96y - 36 =…

A: solution:-16y2-9x2+36x+96y-36=016y2+96y-9x2-36x-36=0  to make perfect…

Q: Find the critical points of f(x) = -2x4 + 2x² - 6 and apply the Second Derivative Test (if possible)…

A: Given problem:- Find the critical points of f(x) = -2x² + 2x² - 6 and apply the Second Derivative…

Q: Find the general equation of the conic with the given properties. 51 59 1. A parabola with directrix…

A: Given: A parabola with directrix y=-5132 and one endpoint of the latus rectum at -18, -5932

Q: (a f (x) + b g(x)) '= a f (x) + b g'(x)

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Q: Q1): Prove that: A square matrix B has inverse if and only determinant of B is not equal zero.

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Q: lim X- 12x²-x-1 1 8x²+2x 4

A: The given limit,         limx→-1412x2-x-18x2+2x

Q: Question 9 If the slope of the tangent line to the graph of y=f(x) at x-a is m(a)=2a+1, and f(1)=5,…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = x² + xy + 4x +…

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Q: 7. Determine the volume of the region that lies under the sphere x² + y² +2²=9, above the plane z =…

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Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: 7 H W N r 1 9 na O 1 2 3 4 5 According to this graph, the function is discontinuous at x = 2. True…

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Q: Consider the following statements 1- The function f defined by f(x) = x³ is decreasing in R 2- If a…

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Q: S tan |2x dx Evaluate

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Q: Question : evaluate the following iterated integrals CLE dy dx

A: In the given iterated integral first we integrate with respect to 'y' and after putting limit of 'y'…

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=-3x²-3xy-8y²…

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: Determine the intervals on which the given function is concave up or concave down and find the…

A: The graph of  y =f(x) is concave up on those interval where f"(x)&gt;0 . The graph of  y =f(x) is…

Q: Directions: Complete the table below based on the given example. Answers for columns 3 to 5 must be…

A: the given problem is solved below in detail.

Q: dy y-x General solution of = dx y+x

A: Solution:

Q: dx ylnx dy || y + 1 X 2

A:

Q: Find a 3 x 3 matrix A such that A A A A = 1 4 0 = 2 0 -1 B-B EL. 0 2 1 = -3 and 0 -5 0 -5 B-B 0 -5 1…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: If given f(3) = -1 and f'(3)=5, the tangent line to the graph y = f(x) at x=3 is y = 5x +16. (a)…

A: This question is based on finding tangent equation at a point on function.

Q: Suppose the position of an object moving in a straight line is given by s(t) = 5t² +4t+4. Find the…

A: Given, s(t)=5t2+4t+4We know that v=dsdt

Q: B. False 4. Which of the following points is not the point of discontinuity of x-7 f(x)= - ?…

A: Given problem:- Which of the following points is not the point of discontinuity of f(x)= (x-7) /(x3…

Q: Evaluate the characteristic w "+k²x ²³w = 0 value of k in the following differential equation w…

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Q: Compute the divergence and curl of F= -(z³-3x)j+4y²k+x²yi

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Q: The best method applicable to find the volume of the region bounded by .x = -y² and x=y-6 revolved…

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Q: . In each part, find polar coordinates satisfying the state conditions for the point whose…

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Q: Which of the following polar equations is symmetric only with respect to the polar axis (x-axis)? r…

A: We need to find the polar equation which is symmetric only with respect to the polar axis (x-axis).

Q: The area between the curve y = 1/x, the y-axis and the lines y=1 and y=2 is rotated about the…

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Q: 2. √√√x + y + xy = 21

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Q: Evaluate the triple integral edV where E is bounded by the parabolic cylinder z = 1 - y² and the…

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Q: Find the volume of the solid generated by revolving the region bounded by y=3/(2√x), y=0 & 1s XS4.

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Q: et R be the region below bounded by the parabola y and y = 0. (0,4) (1,3) R (-2,0) (-1,0) x and the…

A: definite integral

Q: 8/11 Correct While walking in the country, you count 36 heads and 110 feet in a field of horses and…

A: We can find the answer as below

Q: 2 4 cot 4 x dx

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Q: The graph shown is the 1st derivative of function where its domain is R फ़ी An interval where the…

A: topic - strictly  decreasing  interval of function

Q: Consider the two by two system of linear equations x +3y +2y d) What is the coefficient matrix A? e)…

A: Here we will solve the given system of equations,

Q: 1. Determine y(t) if y(0)-0. dy +5 selt- ydt + 2y = 10 What is the value of y(t) in question #1 if…

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Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: Forces of 36N and 50N act upon a body at a 50° angle. Find the magnitude of the resulting force and…

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Q: S x-6 x²+9 dx

A: To evaluate the given integral. ∫x-6x2+9 dx

Q: The graph of a function y = f (x) is shown below. Use the graph to estimate all (there may be more…

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Q: What are the rectangular coordinates of the point whose spherical coordinates are (1,,)? x = 0 y = z…

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Q: Consider the equations 2x - A) x² - 2x x³ +8 0 and B) = 0. x³ - 8 Which of the following statement…

A: We can find the answer in the following steps.