Activity 2: Apply the different theorems four sin 7x 1. lim tan x 2. lim x0 2x 3. lim (cos x - 55*) X+0

Q: 3. Let f(x, y) = xy² + x°y². Find an equation for the tangent plane at (x, y) (-1,2). %3D

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Q: Find the inverse laplace transform of F(s) = 6s/(s^2 + 25) + 3/(s^2 + 25) * %3D

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Q: Find a possible formula for a polynomial of degree four with zeros at (and only at) r -2, 2, 5, and ...

A: topic - polynomials

Q: 1) The slope of the tangent line to the curve y=2/x at the point (4,1/2) is:   2) The equation of ...

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Q: Use your knowledge of the properties of logarithms to match equivalent expressions: bv log, (1) а. т...

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Q: Find one or more values of each of the following complex expressions

A: We need to compute the value of the given expression.          e2tanh-1i

Q: . Find the area bounded by the curve f(x) = (2+x)(x – 5), the lines = -2, line = 0 and the x - axis.

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Q: 3. (D³ + 2D² + D + 2)y = 0

A: The given differential equation is; (D3+2D2+D+2)y=0  

Q: Va – 2 VI + 2 If f(x) = find: f'(x) -| %3D f' (2) = %3D

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Q: Find the oblique asymptote. 7 - x3 f(x) = 2x2 7-x3 2x2 y =

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Q: Find the equation of the tangent line to the curve y 8 sin r at the point The equation of this tange...

A: Given query is to find the equation of tangent line. Since slope of  tangent is given by derivative ...

Q: Let Q (p) : %3D p+1 (a) Calculate the derivative Q' (p) (b) Calculate the quotient Q (p + 4) – Q (p)...

A: Using derivative formula.

Q: Sketch the region that corresponds to the given inequalities.

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Q: Sin zt 2 2 7o47 mous

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Q: Find the volume of the solid whose base is the semicircle y = v4 – x2 where -2 <x < 2 and the cross ...

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Q: y"+12y'+37y=10(e^-4t) @y(0)=4, y'(0)=0

A: Given: y''+12y'+37y=10e-4t So, we can also write as: D2+12D+37y=10e-4t The auxiliary equation is: m2...

Q: A particle starts at point (1, 0, 1) and moves 2 units along the curve defined by a vector equation ...

A: A particle starts at point (1, 0, 1) and moves 2 units along the curve defined by a vector equation ...

Q: One of the parts in the proposed design of a gadget is a tapered cylinder. It is made by decreasing ...

A: To solve the equation for L, 

Q: 8. Find the derivative of f(x) = (1+x³)' ( 14x + - ) using differentiation rules.

A: topic - derivative of a function

Q: How many derivatives at x = a are needed to produce a 5 degree Taylor polynomial centered at a ? O N...

A: How many derivatives at x=a are needed to produce a 5 degree Taylor polynomial centered at a

Q: Students want to clean classrooms. The amount of time (t) it will take to clean varies directly with...

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Q: 6. If f(x) = x³ - x, find and interpret f"(x)

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Q: 5T is equivalent to 12 The expression csc 1- 2 sin? 12 1 Cos 6. - 1- cos 6. 5 2 cos? 6 - 2]

A: Topic = Trigonometry Correct option  csc5π12=21-cos5π6  

Q: 16. 15. sin x cos (x/2) dx 18

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Q: Determine whether it is possible to express 1 as a liner combination of 1= m· 44 + n·91,. for some i...

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Q: 3. Use cylindrical shells to find the volume of the solid eenerated when the shaded region is revolv...

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Q: Find the vertical and horizontal asymptotes of the function f (x) = , where q (x) = (Va+5)(12 –x)² a...

A: Given problem:- Find the vertical and horizontal asymptotes of the function f(x) =1/g(x) where g(x)=...

Q: Use the Shell Method to compute the volume of a solid obtained by rotating the region enclosed by th...

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Q: Which angles have the same sine value? and 3. O T and 3 3 o 4T and 3 - 3 and 3 3

A: As we know that from the trigonometric identities; 1). sinπ+x=-sinx2). sinπ-x=sinx   And 3). sinπ3=3...

Q: Use the trapezoidal rule with n = 4 to approximate cos(x) de

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Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

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Q: termine the equation of the curve whose tangent line at any point (x, y) i and passes A) y = e* + co...

A: We are asked find the equation of the curve.

Q: Find II| y dV, where E is the solid bounded by the parabolic cylinder z = x² and the planes y = 0 E ...

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Q: Directions: Please write your solution on the space provided and boxed The limit of a function Evalu...

A: Since we area given with the multiple number of question and our guideline is solve first question o...

Q: OVIS lhigaimad goinisab A awordz n El 2nibs to s(t) milov ad sd osvig 2000 W x(t)

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Q: Use integration by parts to evaluate the integral: $ds %3D

A: According to integration by parts:

Q: At what point do the curves r (t) = (t, 2 – t, 24 + t²) and r2(s) = (6 – s, s – 4, s?) intersect? %3...

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Q: r each of the following shapes, set up a triple integral you would use to compute its mass, if its d...

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Q: Based on ONLY the table of values above, what conclusion can be made?

A: The given function,   f(x)=x2-4x-2

Q: Question 1 Find the limit. lim, 0(1 + 12x )" where r = 10/x. Write the exact answer. Upload your wor...

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Q: 4. Find the exact arc length over the interval. b. x =y* from y = 1 to y = 4

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Q: direction of maximum rate of increase: Determine the rate of change in that direction. (Give an exac...

A: We have to find direction of maximum rate of increase and rate of change.

Q: Sketch the level curve of the function h(x, y) = y? - a? for c = 25.

A: Here we have to sketch the level curve.

Q: (5x+sin3(4x) + sin(4x³)) dx

A: use differentiation for finding the solution.

Q: Consider the given vector equation. r(t) = 3 sin(t)i + 4 cos(t)j (a) Find r'(t). r'(c) = (b) Sketch ...

A: Solution of question is written in step2.

Q: 2. ху 4 a. when x=8 10 dx b. when x-1 dt dy dt -6

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Q: f(x) = (8x + 10)*, then find the second derivative, f" (x) =

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Q: Write a full soultion  Let f(x) = 1− x/x+1 A) Find the domain and the range of the function f.

A: Topic = Functions   Domain x∈-∞,-1∪-1,∞RAnge fx ∈-∞,-1∪-1,∞

Q: 9. The three midpoints are given as shown below. A (X), y1) D(-7, 6), F (2, –2) G (x, y) B E (8, 5) ...

A: Since you have posted multiple questions , as per our guidelines we will answer the 1st question for...

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 5 sin(3x) sin(6x) dx

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