Evaluate In x x (4 - In² x) - In 14- In² x | +C - 2 In 14-In² x | +C 12 -dx In | x (4- In²x) | +C In 14-In² x | +C

Q: Given f(x,y)=x2y³-4y, find the directional derivative at the point (2,-1) in the direction of v=.

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Q: *y=(2x^2+6) find dy\dx 4x\(2x^2+6) O 6x O 4x\(2x^2+7) O

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Q: The table below shows values for four differentiable functions. Suppose we know the following…

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Q: of the given conditions. lim f(x) = ∞, 210 Limits at Infinity - Horizontal Asymptotes Sketch the…

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Q: Derivative app The given rectangle has a perimeter of 60cm. Find the values of x and y that result…

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Q: Find the volume of the given solid. Under the surface z = 1 + x²y2 and above the region enclosed by…

A: To find the volume of the given solid.

Q: 6. f(x-1) dx/(x+1)

A: **As per our guidelines, we are supposed to answer only one question at a time. So, we will solve…

Q: If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then…

A: The volume of the water remaining in the tank after t minutes V=50001-t402  gallons

Q: Evaluate sec(log x) -dx x In | sec(log x) + tan(log x) | +C 1 log e In | sec(log x) + tan(log x) |…

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Q: Question 4 (a) Solve the following: (b) Explain with the aid of a sketch how this value can be…

A: Above question is solved.

Q: Identify the number of significant figures (sig figs) in each of the values. I sig fig 2 sig figs 3…

A: We can find the significant figures.

Q: or each function h(x), find two functions f(x) and g(x) such that h(x) = f(g(x)) a) h(x)=√x² + 3 b)…

A: Topic:- function

Q: Find the arc length of the curve on the given interval x (0) = 0³, y (0) = 0² ; 0 ≤ 0 ≤ 2

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Q: If f(x) = 5³x then f'(x) = 5.A 5h 3 In S O 3x(5³-1) 5³ (In 125) 3(5²)

A: Here, the given function is: f(x)=53x So, note that ddx(ax)=axln(a) where a is a constant.

Q: Q22) The inverse Laplace transform of H(s) : = a) f(t) ==e¹+¹e²t 8 8 -3 c) f(t) == est +²e-2t 8 8 1…

A: To find the inverse laplace transform of givem function.

Q: 7-10 Verify the given linea determine the values of x for accurate to within 0.1. 7. √√/1 + 2x 1 + x

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Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a<b means that a…

Q: Question 4 (a) Solve the following: √4x¹dx (b) Explain with the aid of a sketch how this value can…

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Q: Which of the following statements is true about g(x) = 8 at x = 8? O g(r) is continuous at x = 8 O…

A: Consider the function  g(x)=x+8x-8

Q: Find y' given that y - y' sec²√x tan√x √x y' = 2sec√x tan² √x y' = 2tan√x sec² √x sec√x tan√x y' √√x…

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Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

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Q: Given the function f(x) = -2x + 6x within the interval [0,8], at what values of x do the absolute…

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Q: 7) If f(x) = est cosx find f'(0).

A: Derivative of a product of two function isf(x)=g(x)h(x)then f'(x)=g'(x)h(x)+g(x)h'(x)

Q: Find an equation of the line tangent to the curve tan¹(y) = (x+y)e at the point (0,0). tan ¹(xy) =…

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Q: B. Write in Signe Notation 1.-244-3 42 50 times 2. 1 + 9 + 25 + 49 +81 ++ /2/ }} + { + } / + 2/ 23…

A: Let's write given series in sigma notation.

Q: 4) a) Determine the derivative dx of the following functions y = 3** b) 1-3- 3e² 1² c) y d) y =…

A: We have to find the derivative.

Q: Pls help ASAP

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Q: Find the extreme values of the function f(x) = (x² + 2x)³ on the interval [-2, 1].

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Q: Marine Vessel A is 20 km west of another Marine Vessel B. If Vessel A sails east at 10 km/hr and at…

A: Marine Vessel A is 20 km west of another Marine Vessel B. If Vessel A sails east at 10 km/hr and at…

Q: Find the distance from the point (-6,2,-7) to the plane -x + 4y = 2z = 22.

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Q: Determine the slope of the tangent line to the curve of sin(x + y) = y2cos(x)  at  the point (x,y) =…

A: Topic = Derivative

Q: bn gn-4+5 10n

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Q: integral

A: We will find the solution m

Q: Question 5 limx→→+∞ (1 + ¹)² O ll SO III OIV O Not Indeterminate

A: Please mention also what the first four options wants to represent here ...as correct answer is e .

Q: The angle between the vectors [√2 – 1, √2 + 1, √2] and [1, 1, 1] is: 45° 60° 90° 30°

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Q: Determine the critical point/s of f(x) = ln(x2 + 4x + 14) on [-4, 2]. ΟΧ -- -2 Οχ -3

A: Given, f(x)=ln(x2+4x+14) on [-4,2]

Q: * The following matrix is a 100 020 0 004 identity matrix O skew symmetric matrix O none of these O…

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Q: 3. Find the derivative D(x *arctan(x)) And the integral 6x dx 9+x

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Q: 5 ;ㅣ

A: We have to find first four terms of give series.

Q: 5: Evaluate I where D is the rigion bounded by xy ve x+y = 7 SS (X+Y) DA D (1

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Q: Find the final value of the system corresponding to 3 (s + 1) y (s) = s (s²+2s + 10) 2 O 0.3 0.6 O 3…

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Q: a. g(3) = = b. lim g(z) C. lim g(z) d. lim g(z) = Z-1 = -4 -3 -2 -1 10 6 2 0 -2 -4 -6 9(z) 2 3 5 6

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Q: A Л The path r(t) = (4 sin t) i + (4 cos t) ] describes motion on the circle x² + y2 = 16. Find the…

A: The path r(t)=4 sin ti+4 cos tj

Q: How firel the center, foci, vertices and eccentricity for the following equations! x+4y²-4x-8y +4=0…

A: Concept: Ellipse: The equation of the ellipse with center at (h,k)  (x-h)2a2+ (y-k)2b2 =1 Hyperbola:…

Q: 2. A 6-ft tall man is walking away from a 15-ft post at a rate of 5 ft/sec in a straight line. How…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: Calculate the direction of P1P2 and the midpoint of line segment P1P2. P 1(3, 4, 6) and P 2(6, 0, 1)…

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Q: 3) Given y(0) = 1 Over what area are we guaranteed a unique solution? Explain using existence and…

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Q: 12 1= A ✩ = OÅ and √ – OẺ . Then, AC is equal to: U= = Oa)-7-7 Ob)-7 Od-+7

A: Topic:- vector algebra

Q: H.W: Estimate the root of the equation for the following equation usind Newton- Raphson method: 1…

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Q: Solve the following equations 2)3x+2 = 27 1) 2Ln(√x + 3) + 2Ln(√x-1)=Ln(6x-7) I 1 1

A: Let's solve both equation.