Find the equation of tangent line to the curve f(x) = x² at x = 3.

Q: Graph all vertical and horizontal asymptotes of the rational function. f(x)= x²+2x-3 2x² +3

A: I have appended the formula used in the solution part of the question

Q: Find the differential equation such that y(x) = c₁(x-4)³ + c₂ln(x-4) (x-4)² 64x²d²y + 2 +60x+y=0 dx²…

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Q: Find the derivative of the following function. 3 8x y = In x y'=0

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Q: Q3)Evaluate the following integral by using Trigonometric Substitutions Method. dx y = S₂ 9x² +9

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Q: R: y = 2x +1,x+y=7,x = 8

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Q: Q7) Calculate AC. BC and (A + B)C. Also, verify that (A + B)C=AC + BC 6 71 [0 1 1] B= 1 0 2 If A =…

A: Follow the procedure given below.

Q: Evaluate x³ + €

A: On solving this we will get

Q: The position function of a particle is given, in metres, as s(t)=t 4-10t 3+36t 2+10t+12 where t ≥0…

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Q: The function f is defined as follows. X if x #0 f(x) = 2 if x = 0 (a) Find the domain of the…

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Q: Q3. Find the cross product of the vectors and .

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Q: Determine the center and radius of a circle given that its equation is x² + 12x + y² - 6y = 4 Use…

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Q: Q2: Fill the blank: 1) lim (1+)5x x48 4x 2) lim x.e-3x = X-8 3) (csch-¹x³) = = 4) ₂° e-*dx 5) S-…

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Q: Use long division to divide. (Simplify your answer completely.) (8x237x - 15) + (x - 5) X = 5

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Q: 24) Find dy /dx for the following functions : a) y². cotx= [sin(x,y)]-¹ b) y = (lnx + x) tan x

A: Given: a)y2·cotx=sinxy-1b)y=lnx+xtanx

Q: Q5) Evaluate the following integral by using Partial Fractions Method 2x²-3x+2 y =S₁ dx (x-1)².…

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Q: Find the time it takes for $9,800 to double when invested at an annual interest rate of 18%,…

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Q: Find the exact length of the curve. 1 y = 1 + cosh(8x), 0 ≤ x ≤ 1 8

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Q: Below is the graph of y=e*. Transform it to make the graph of y=-e* +5. Give the domain and range of…

A: Given problem:- Graph of y = ex   Transform it to make the graph of y = - ex + 5   Give the domain…

Q: Use Lagrange multipliers to find the absolute maximum and minimum values of the function z = f(x, y)…

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Q: 7) Write an expression that can be used to find the average value for the function g(x) over the…

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Q: 2. Determine the points on the curve f(x) = sinx-cosx, 0≤x≤27 where the tangent line is horizontal.

A: Find out the points where the tangent line is horizontal.

Q: Evaluate the integral: LIVE 1 I√9r²+25 dr.

A: We will solve the given question using simple Integration rules.

Q: f(t)=16t²+361t+ 12 is the height (in feet) of a ball launched straight up t seconds after it is…

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Q: Solve the initial-value problem y"+5y'+6y=0, y(1)=2, y'(1) = 3

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Q: 6. If q p² p³ - 1 9² p2 µ³ – 1 1 = 0, show that pqr = 1. - 22

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Q: Suppose that the marginal revenue from the sale of x units of a product is MR = R'(x) = 3e0.01x.…

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Q: 3. The trigonometric sin cos coscos O2 cos cos O2 sin sin expression sin (0+) is equal to + cos sin…

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Q: Please find the gradient of f(x, y) = ln(x² + xy²) at (2, 1)

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Q: Use the One-to-One Property to solve the equation for x. (Enter your answers as a comma-separated…

A: We use the property of the log function to determine the value of x

Q: 5 (x+4)³ For the function f(x) = exist, enter Ø as your answer. X -4.1 -4.01 -4.001 -4.0001 -4.00001…

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Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

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Q: Find the directional derivative of f(x, y) = √√xy at P(3, 5) in the direction of Q(3.920, 0.795). 1.…

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Q: Use the root test to determine whether the series converges or diverges. If the test is…

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Q: Solve for x: |x+5| < |X-71

A: Follow the procedure given below.

Q: 8 Y + 2√² + 2y = 10x + 25

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Q: 5a) Which of the following vectors are unit vectors? Justify your answers. *-[243] b) Are these…

A: A vector that has a magnitude of 1 is called unit vector. For a given vector v→= x,y,z magnitude is,…

Q: Determine the value of f(-3) for the function f(x) 00 O Undefined 3 B O 15 O x³ +18x²+104x + 192 for…

A: I am attaching image so that you understand each and every step.

Q: 1 If f(x) has an inverse function f-¹(x), could either the graph of for the graph of f-¹ be…

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Q: дуту (x) 415 = к+к ht

A: We need to solve D.E.

Q: Find the exact length of the curve. 1 y = + 10x37 6 1 ≤ x ≤ 3

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Q: Find the intersection of the line 1₁: x-6 2 || y+2 1 with the plane p: x-6y - 2z - 10 = 0

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Q: Consider the following. f(x) = =x+4 (a) State the domain of the function. O all real numbers x O all…

A: We have to find asymptote

Q: 3 -6 -4 -3 4 Let y = V1 = 1 5 -1 Compute the distance d from y to the subspace of R4 spanned by V₁…

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Q: 4. If x - 2y = -1 and x + 2y = 3, then a +y is equal to O 1 O ♡

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Q: 3. Evaluate f sin(3x - 1) dx

A: we want to determine the integral  ∫ sin(3x-1) dx

Q: By using Euler method, Solve these questions 3.3 2 2 XD² + 2XD + XD=Y=6

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Q: Effect of Housing on Start Jobs The president of a major housing construction firm claims that the…

A: This question is related to rate of change, we will solve it using given information.

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges.…

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Q: 2a)Use triple scalar to verify that the following vectors are not coplanar. a=[-2,1,0], 5=[-3,4,5],…

A: Given problem:- 2a)Use triple scalar to verify that the following vectors are not coplanar.…

Q: Q8. Find all the first and second order partial derivatives of the function f(x, y) = x sin y + y…

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