Find all local maxima, local minima, and saddle points for the function: f(x, y) = x – 6xy + 8y

Q: #6) Deler mine whether converges diverges, Calculatk limit an n+3

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Q: *Introduction to Derivatives (x²+2x-3 if x#1 (4 Using the 3 conditions, show that f(x) = is both con...

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Q: Q) Let û = 2745, Vz+3 , and w=T-5 find Scalars a and b such that u - av + bw

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Q: If f(x) = In(3x + In(x)), find f'(1). f'(1) = 0

A: Given :f(x)=ln(3x+ln(x))

Q: 3. lim f(x) lim f(x) 4. lim f(x) lim f(x) = -2, = +0, x+3- = 2 and f(2) = 0 = -0O x-2+ x+3+

A: Let's find. 

Q: 1 (x-4)°(x² +9)²

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Q: 32. (a) For a = 1, 2, and 3, draw position vectors for (1) ð = a²7 + 63 (ii) = 57 – a²3 (b) Explain ...

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Q: Inverse Laplace Transform; f(s)= 1/s-3

A: Laplace Inverse Transform of 1s-3

Q: (2) Compute the following integrals. /4 (a) sin (4r) cos (4.r) dæ. (b) cos(ka)e-lz dx, Hint: conside...

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Q: Evaluate the following indefinite integral. Use C for any constant of integration. 68x dx J 8x² – 10...

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Q: (2+7sin 2 dr 3. Co s 2

A: Given: I=∫2+7sin3zcos2zdz We know that the trigonometric identities; 1). sin2θ+cos2θ=12). 1cosθ=secθ...

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Q: Use integrable combination: y(2x+y^2)dx+x(y^2−x)dy=0

A: Given :y(2x+y2)dx+x(y2-x)dy=0

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Q: 16. Suppose that over a region of space the electrical potential V is given by V(x, y, z) = 5x? – 3x...

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Q: An = e¯" cos(nT) %3D

A: Here, note that -1≤cos(nπ)≤1 So, -e-n≤e-ncos(nπ)≤e-n...(1)

Q: 7.4 Q7.4 Find the taylor series for fcx) = centered at a= 2 (-1)**1 (1 + 1) 00 (A) Σ (x- 2y (B) E (-...

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Q: Assume that 0 is an angle in standard position whose terminal side contains the point (-8,15). Find ...

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Q: ACTIVITY 1: Practice ! Apply differentiation rules in finding the derivative of the given functions....

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Q: 12. cosx(1+ tanx)² = secx + 2sinx %3D

A: Prove : cosx ( 1 + tanx)^2 = secx + 2 sinx

Q: Identify the point (xo, yo) on the line 7x – 12y = 10 that is closest to the origin. (Give your answ...

A: Identify the point (x0,y0) on the line 7x-12y=10 that is closet to the origin. 

Q: Q2) if the vechrs V=-i +5 and ū=Tz i+5J+2 R Find a) The scalev component of ū in the divection of V ...

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Q: 12. lim [(x 5) - 3x] isOHOAHOH 3OH2 UA a. lim (x 5) + lim 3x IROCORO b. lim (x- C. X-5- lim 3x X-a -...

A: 12)limx→a[(x-5)-3x] = limx→a(x-5)-limx→a3x13) limx→1x2-2x-3x-2=12-2.1-31-2limx→1x2-2x-3x-2=1-2-3-1li...

Q: 2. An iPhone 13 pro max is dropped from the top of the Balayong Park monument, 225 ft high. (a) How ...

A: This question can be solved by using the equations of motion.

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A: The altitude of a triangle is increasing at a rate of 1 cm/min. The area of the triangle is increasi...

Q: arctan x dx (けx) It X

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Q: y" - 9y' = 0 Determine the Characteristic Equation for the differential equation. (A R² – 8 = 0 B R2...

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Q: 1. Use the graph of the function below to answer the following: -6 -5 -4/-3 -2 1 2 /3 4 $ 6

A: According to grapha. f1 =2b. limx→2+fx=-3c. f2=1d. limx→0fx=-4e. f3=12f. limx→-1.5fx=0g. f4=2h. limx...

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A: Here we have, The length of a rectangle is increasing at a rate of 2 ft/s, and its width is increasi...

Q: Find the derivative as indicated: 1) y = 3 cos x +2 sin x; find y' 2) f (t)-t sin t find f' ()

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Q: The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per y...

A: Given population of world in 2015  was 9.75 billionlet   for t=0 , we have year 2015

Q: 1. Without a table of values and without graphing f(x), give the values of the following limits and ...

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Q: Find the radius of a cylindrical can (with a lid) to contain 1728 cm³ of water, using the minimum am...

A: This is a problem of mensuration. Based on the general formula of volume of cylinder we will calcula...

Q: Find the area of the region bounded by y = la, y = 0, x = 0, x = 2 %3D Give your answer to the neare...

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