1) Use the second derivative test to classify any critical points and determine whether each critical point is a local maximum, minimum, saddle point, or none of these. f(x, y) = 4x² +9y² +8x − 36y + 24

Q: 13. Using synthetic substitution, find f(x) when x=-5 for f(x)=2x¹ +5x²-3x² +6x-9. You must use the…

A: f(-5)=511Explanation:Write the coefficients of x in the division box

Q: Solve the following:- 1. Find Maclaurin's series f(x) = e√2x. 2. If f(x, y) = 0, find is - d²y dx²

A: The objective of the first part of the question is to find the Maclaurin's series for the function…

Q: a. 3+4+5+...+93 +94 b. 3+6+9+...+30 c. 9+16+25+36+...+144

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Q: Evaluate the following integral using trigonometric substitution. 11x² dx 2 (49+x²)² S.

A: I=∫11x2dx(49+x2)2

Q: Geometric series can be found by transforming f(x)= to series form using 1 4 Maclaurin's series to…

A: The objective of the question is to understand why the geometric series diverges at x = 4 and x =…

Q: ܘ 34.

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Test the series below for convergence using the Ratio Test. n=1 n+3 34n+4 The limit of the ratio…

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Q: Peter wishes to create a retirement fund from which he can draw $40,000 when he retires and the same…

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Q: Find a parameterization for the curve y = 6 + 2x¹ that passes through the point (0, 6, -5) when t =…

A: To find the parameterization of the curve

Q: Use the substitution t= In(x) to transform the given Cauchy-Euler equation to a differential…

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Q: Let E be the solid region in the first octant that lies inside sphere x 2 + y 2 + (z − 1) 2 = 1. The…

A: The objective of the question is to describe the solid region E in cylindrical and spherical…

Q: What are all values of a for which the series Select one: O a. 9 15 O C. a < 12 O d. a <9 3 X k=0…

A: The given series is .The aim is to find the values at which the given series is converges.

Q: A farmer has 1,600 feet of fence and wishes to build two identical rectangular enclosures, as in the…

A: We need to find out the dimensions of each enclosure when the total area is maximum, also the area…

Q: Given the following quadratic function in general form, f(x)=2x² + 12x + 1 Complete the square to…

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Q: 9. (a) A gardener is building a fenced in rectangular garden against a wall of his house. If he does…

A: Answer No. (a): A gardener is building a fenced  in rectangular garden against a wall of his…

Q: a. lxldx b. (1+x1) dx

A: To sketch the graph of the integrand function and by using it to evaluate the integral.

Q: (BC Topic) (Technology Permitted) If the sum of the series Σ 3 first four terms, what is the maximum…

A: The error found by the formula : |error| ≤ an+1 Here, error is estimated by the sum of the first 4…

Q: 12. Write 18(cos169° + isin 169°) in rectangular form. Round numerical entries in the answer to two…

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Q: Let �(�)f(w) be a function of vector �∈��w∈RN, i.e. �(�)=11+e−���.f(w)=1+e−wTx1​. Determine the…

A: The objective of this question is to find the first derivative and the matrix of second derivatives…

Q: cos3tdt d. tantdt

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Q: a. Evaluate 4 tan 2x sec ²2x dx using the substitution J u = tan 2x. b. Evaluate 4 tan 2x sec ²2x dx…

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Q: 6. Evaluate the indefinite integral using partial fraction decomposition. Sx² Mo x-13 x² - 6x +5 5)₁…

A: Given Indefinite Integral is as follows

Q: Do the following with the given information. ²2 23 cos(x²) dx (a) Find the approximations Tg and Mg…

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Q: Determine the interval of convergence of the following power series (−1)n-12n+1 Σn=0 (2n+1)! ²

A: The objective of this question is to find the interval of convergence for the given power series.…

Q: Find the limts of the following problems.  (a) an= tan^-1(3n/sqrt(9n^2+4))  (b) lim as n-&gt;…

A: (a). 4π​(b). 1Explanation:Step 1: Step 2:Step 3:

Q: 9. Find the interval of convergence and radius of convergence of the series n=1 2n (x - 1)n n

A: The objective of this question is to find the interval of convergence and radius of convergence of…

Q: x² -dx. X-4

A: I=∫x2x−4dxSubstitution u=x−4Using the power ruleddxxn=nxn−1

Q: Use one of the reduction formulas shown to the right (which are valid for a # 0) to evaluate the…

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Q: Write an equation (any form) for the quadratic graphed below -5 -4 -3 -2 y = 1 2 1 -1 -2 -3 -5+ 2 3…

A: Answer is in the below box. If you have any doubts at anywhere in the explanation or answer please…

Q: Help evaluate the following integrals please

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Q: 8 The graph above shows the base of an object. Compute the exact value (in terms of ) of the volume…

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Q: 16. A piecewise function always has a jump discontinuity.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Match the graph of the function on the right with the graph of its derivative. Choose the correct…

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Q: let f(x,y)=(5x-y)^7 then ∂^3f/∂x∂y∂x

A: The given function .The aim is to find the mixed partial derivative .

Q: Eliminate the parameter & to fcys for - form x= [2(t) = 51² | gets = 2 + 2t find a Cartesian…

A: To eliminate the parameter t to find a Cartesian equation in the form  for the parametric equations.

Q: Find all the second order x f(x,y) = Z²+y х+у partial derivatives

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Q: The key point (-12, 4) is on the graph y = f(x). What is its image point under the transformation g…

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Q: #15 & 16: Solve each inequality using a number line sign chart. Write answers in interval notation.…

A: (−∞,−7)∪(−7,0)Explanation:(16) If you have any problem let me know here in comment box for this…

Q: Graph the set of points of discontinuity for the following function: f(x, y) = 1 xy-3

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Q: Find all critical points of the function f(x) = x² − 2x² - 54x + 1. (Use symbolic notation and…

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Q: Evaluate the following integral. 16 0 1 + √√x dx

A: I=∫0161+xdxI=∫016x1+xxdxSubstitute 1+x=u2

Q: The probability of precipitation in a California city varies from a peak of 0.38 (38%) in January to…

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Q: Please solve the following calc 3 problem

A: The objective of this question is to find the component form of the velocity of the airplane. The…

Q: Σ H=I Τ n(n+1)

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Q: suppose the general solution is y(t)=yc(t)+Y(t), where yc(t)

A: Given data is suppose the general solution is y(t)=yc(t)+Y(t), where yc(t)=

Q: If f'(x) = 10x⁹, what is f(x)? (Remember the constant of integration.) f(x) = X

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Q: In 2005, Dr. Larry Kamin and his botany students at Benedictine University collected the following…

A: a) H(D) = 5.629D0.713 feet b) 91.579 feetExplanation:Step 1: Obtain the regression output Enter the…

Q: Find all critical points of the function f(x) = x-² - x-³. (Use symbolic notation and fractions…

A: Need to find out the critical points for the given function.

Q: The rate of change in data entry speed of the average student is ds/dx = 2(x + 4)-1/2, where x is…

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Q: Find the arclength of the curve r(t) = (3t², 2√3 t, lnt), for 1≤t≤ 10. L =

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