C) Find a z and of xy" ay (xy2) - -군3 COs %3D

Q: y = 2 (x² – 3x) (a) Find dy/dt when x = 2, given that dx/dt dy/dt = (b) Find dx/dt when x = 7, given…

A:

Q: Evaluate the following. Give an exact answer, not a decimal a a) csc 2 b) sec ä

A: Topic:- trigonometry ratios

Q: Barbados A cruise ship maintains a speed of 5 knots (nautical miles per hour) sailing from San Juan…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: When estimating distances from a table of velocity data, it is not necessary that the time intervals…

A: We have to find the Distance

Q: Problem #2: Differentiate f(x) = [(3x* – 5)(2x³ + 9x – 6)]° and solve f '(2). Solution: Reason:

A: Solve the following

Q: y = x' cosx

A:

Q: The position of a particle on the x-axis is given by (t) = t – 4t + 3. At what time is the…

A: solution:-position of particle is given byx(t)=t2-4t+3velocity, v(t)=ddtx(t)…

Q: Find the second derivative of + e® sin y + 3xy = 0 y? %3|

A:

Q: Consider the solid of revolution obtained by rotating the region inside x2 + (y – 4)² = 9 about the…

A: Given problem:- | Consider the solid of revolution obtained by rotating the region inside x² + (y -…

Q: Solve the following:

A:

Q: 13. sin? 4x cos² 2x dx T/2 14. S sin? x cos³ x dx

A:

Q: P7: x3 + x – 1 dx J x(x – 1)(x + 5)²

A:

Q: (#2) Evaluate the directional derivative Duf (3, 4) if f (x,y) = Vx² + y² and u is the unit vector…

A: The expression for the directional derivative of the function f in the direction of u at a point…

Q: ら)1f u-L -*9 sin (2x ty), x = s? + 2t" and y= 2s -t" au using at find the chain rule Ond as

A:

Q: 3. Which of the following integrals cannot be evaluated using a simple substitution? 1 xp- x +1 ,4 1…

A:

Q: ydy 3. Jo (a2 – y2)z

A: Topic:- integration

Q: Two automobiles start from a point A at the same time. One travels west at 80 km/hr and the other…

A: Topic:- application of derivatives

Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² – c² and y = c² – x² is…

A:

Q: Using chain rule, find the derivative of the hyperbolic functions: f(x) = tanh(4x) f (x) = In…

A:

Q: da a 2 +10a+25a 2

A: Given,  ∫ 1a32+10a+25a12da

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A:

Q: 3 csc x cot x dx 3

A: Given query is to find the integral.

Q: (с) (2x3 + у) dx — x dy %3D0..... [EXACT DE]

A:

Q: 2. The Auxiliary Equation : (4D - 4D' - 23D² +12D+36)y = 0

A: Topic:- differential equations

Q: 1) Calculate 21+v3i

A:

Q: əf. dy and In each of the following, find dx (n) f(x,y) = tan x tany %3D

A:

Q: x2 dx - 1

A: See the details solution in below

Q: A piecewise function is given. Use the properties of limits to find the indica fix) if x 3 5. if x-3…

A:

Q: 1) Consider the DE x²y" – xy - 15y = 2x - 4 %3D | A) Verify that y = x and y2 = x x-3 satisfy the…

A:

Q: ind an antiderivative of the following function by trial and error. Check your answer by…

A: We have to find integral

Q: 8.) What is the slope of a tangent line tangent to curve g(x) = v5x -8 at point x= 37 a.) 7 b)V7 d.)…

A: Since you have asked multiple questions, we will solve the first question (i.e., Question-8) for…

Q: If h(x) = V6 + 5f(x), where f(2) = 6 and f '(2) = 3, find h'(2). %3D h'(2) = %3D

A:

Q: 1 ): The vectors 2 and form a basis the vector space R'. Select one: O True O False

A: Here we state whether it is true or false.

Q: evaluate the integral - sin (x) dx (x) 1- sin |3|

A: The given integral,      ∫sin(x)1-sin2(x)dx

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 4 sin(t). The initial…

A: We have to find the velocity, displacement and total distance.

Q: 2x2 ) 3x Evaluate the given limit of lim if it exists. 1 x +1 O 1 O limit does not exist 2

A:

Q: A cylindrical container with both ends closed has a radius r cm and a volume 100 cm³. Determine the…

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Q: . Evaluate [10x cos(x²) dx . A) sin(x³)+C C) 30 sin(x') +C 3 B) sin(x') +C 10 D) 3 sin(x') +C 10

A: Our Aim is to evaluate the integral given below:-∫10 x2 cos (x3) dx -(i)

Q: Researchers found the demand for cheese in a particular country for a particular year can be…

A: The equation is given by lnq = D-1.32lnp                                 ........1 Where, p…

Q: 2. The Auxiliary Equation : (4D* – 4D' – 23D² +12D+36)y = 0

A: Given: 4D4-4D3-23D2+12D+36y=0 So, 4m4-4m3-23m2+12m+36=0

Q: Convert 130° to radians. Evaluate sin A if cos A – ? (5 and

A: Please refer to the image below

Q: At what point on the line y = b does the line segment from (0,0) to ( a,0) subtend the greatest…

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Q: Find the area of the region bounded by the graph of f and the x-axis on the given interval. f(x) = x…

A:

Q: Areas

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Q: 3 of 7 f(x) = {x - 2, *5 3 x+4, %3D is continuous everywhere. x > 3 O false O true

A: Given query is to find function continue or not

Q: P8: sin x cos x -dx J (2 sin x – 1)(sin x + 1)

A: ∫1au+bdu =1a lnau+b+C

Q: . Evaluate sin 0 if cos 0 = 2/5 and 0 is in quadrant I. %3D Evaluato 000 A if

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Q: Find the equation of the tangent line at the given value of x on the curve. 3 4 2y° + xy - y =…

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Q: Find the derivative of f (x) = 1+ er e* A. ex+1 C.E (e*+1)² E. None of these В. ex+1 D. (1+ e*)²…

A:

Q: 00 n2+9 E(-1)"-1 n2+ 8 n=1 a) Show that the ratio test fails b) Test the given series for…

A: