A plane is defined by the equation x - 7y - 18z = 0. a. What is a normal vector to this plane? b. Explain how you know that this plane passes through the origin. c. Write the coordinates of three points on this plane.

Q: 1. (3x - 2y + 1) dx + (3x - 2y + 3) dy = 0.

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: 3. Sxsin x dx

A: topic- indefinite integral

Q: For what values of a are the vectors (4, -2, a) and (9, a², a) orthogonal? O -6 and 6 0 O -2√3 and…

A: Equate dot product of two vectors to zero

Q: Tutorial Exercise Calculate two iterations of Newton's Method to approximate a zero of the function…

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Q: (3x-1) dx 2x²+2x+3

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Q: Given the function  y = 5 arcsin(x),  find  y'.

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Q: . A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F.…

A: . A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F.…

Q: All exponential functions can be written in many forms. Write the function -0.08t f(t) = 340e- in…

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Q: Find the area of the region enclosed by the cardioid r = 2(1− sin θ).

A: Given:  r = 2(1− sin θ)

Q: Question 7 (a) Find if x² + y² + xy = 1 dy dx (b) Identify the nature of the stationary points of…

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Q: + R (+) et sinti-etcost] a) Find the velocity and acceleration vectors. 6.) Find the speed,…

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

Q: The function f(x) = = √x 2+√√4x is. increasing on its natural domain increasing on (2, 3) and…

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Q: 5. r(x, y) = ln (x + y)

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Q: Solve for the homogeneous linear equation given below 1. xydy- (x + 2y)² dy = 0 O-In ()-4lny = C…

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Q: Problem 2. Find an equation for the tangent line to the curve y = 2x² + x3 at x = 4. You must use…

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Q: -2, if x < -1 f(x) = (x + 1, if x ≥ −1

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Q: The percentage of people of any particular age group that will die in a given year may be…

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Q: 1. f(x) da converges, then If f(x) ≤ g(x) for all z in [a, +∞o) and converges. g(x) dx also

A: Given

Q: For each of the following functions, do t a. Determine if f is continuous at a. Determine if f is…

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Q: Suppose A = 4i-6j, B = i + 7j, and C = 9i - 5j. Then the scalars h and k such that A = hB+ kC are…

A: Topic = Vector

Q: Find the nth Taylor polynomial for the function, centered at c. 1 f(x) n = 4, c = 2 +2² P4(x) = = =

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Q: 3 Jess bought a new car for £12 000. In the first year the value of the car depreciates by 20%. In…

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Q: Find the derivative of the trigonometric function. Use the chain rule. f(t) = 5 sec9(pi(t) − 4)

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Q: Obtain the TSE of f(x) = 2x² in powers of (x-1)

A: To Find: The Taylor Series expansion of function 2x-2 with center x=1

Q: 1. [(5x (5x - 3)100 dx 2. [(x − 3)¹/4 da dx 5 3. · / ( 2² + ² ) ( ²2 2²³ + 2) * dx 2 3

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Q: I. Find the general solution of the following: 2x* 1. dx 2.d = xy 3. dy = (6e³x + 1)dx

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Q: 7. S d.x 25x²+36

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Q: 6. Evaluate the following multiple integrals. π +2 (a) y sin(xy)dady (b) [1² fr esc² 0dødr π/4 π/2 ©…

A: As per our guideline we have to solve only first three parts

Q: 2. If function f(x) = 3²-12 is continuous at x=2, find f(x). x-2

A: We need to find f(x).

Q: Find the distance between the points. (−14, 1), (1, −7)                     units

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Q: 2 ind the arc length for f(x) = 6-2 x² over the interval [0, 2].

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Q: Question 7 AL Given that APOBDEA and APOCA are semicircles with centre O and P respectively. AP = 10…

A: We can solve the given question by the help of trigonometry.

Q: xy = 1, y = 0, x = 1, and x = 2 is rotated about the line x=-1.

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Q: Find the tangent line approximation for √1+ x near x = 5. y = ||

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Q: A turkey is removed from the oven when its temperature reaches 185°F and is placed on a table in a…

A: Given problem:- A turkey is removed from the oven when its temperature reaches 185°F and is placed…

Q: Jse the definition of derivative to find f'(x) where f(x)=√x

A: Given,  f(x)=x

Q: π Determine the Taylor series for f(x) = sin x about x == 3

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Q: For the function f(x,y)= x + 4y 3 4 x +y find f, fy, f(5,-5), and f,(1,3).

A: For the function fx, y=x2+4y3x3+y4, to find fx, fy, fx5, -5, and fy1, 3.

Q: Consider the triple integral JJJ (x+y+z)dV E where E is the solid enclosed by the cylinder x² + y² =…

A: Let's solve A and B part.

Q: Question 6 (a) Use the Maclaurin series, In(1 + x) = x -+-+-=-1(-1) ¹+¹ ² 1+2 to derive the series…

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Q: (a) Find if x² + y² + xy =1 dy dx (b) Identify the nature of the stationary points of y=4x³ - 21x²…

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Q: Determine the antiderivatives of the following functions: 4. f(3x² +1)4 x dx 5. s dx

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Q: y = 3-x²

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Q: What is the coefficient of the second term in a binomial that is raised to the sixth power?

A: Given.

Q: 8. · √(x) √₁² 1 9. J 5x + 1 dx 10. S 3x +9 (x) √√x² - 1 dx dx

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Q: -: Show that -1+i√3 =1 for all combination of signs.

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Q: Show that the points form the vertices of the polygon. right triangle: (−4, 5), (0, 7), (2, 3)…

A: The given points are -4,5, 0,7, 2,3

Q: 4. A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t = 0,…

A: Above question is solved.

Q: Find the absolute extrema of f on the given closed interval. 1. f(x)= x³ + 3x² - 9x ; [-4,4]

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Q: 7. favn-1dr 8. (1) Vai - dar 1 f sh 1 9. dx 5 + 1

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