1 dx x² – 1 C3 5. . J2

Q: Verify the given linear approximation at a = 0. Then determine the values of x for which the linear ...

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Q: Find the third derivative of the function: Y = =+ VX3 %3D

A: To find the third derivative of the function: y=1x+x3  

Q: For the sequence {an}, with lim an = 9, this means the terms in the sequence approach 9 as n becomes...

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Q: 4x-1 4x-1 Calculate lim and lim If the limit does not exist but can 8х-5 8х-5 x→-00 be described as ...

A: Here, to evaluate the given limits  limx→∞4x2-18x-5  &   limx→-∞4x2-18x-5

Q: Question 3 Determine whether or not each of the following sequences is (i) bounded, (ii) monotone, a...

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Q: Given the differential equations functions f(x) and g(x), and their derivatives in the table below, ...

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Q: Evaluate the following integral: J Sec?x -dx V1-tan2X

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Q: The doubling period of a bacterial population is 20 minutes. At time t = population was 90000. 100 m...

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Q: 10* (100* + 1)dx

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Q: Solve the given differential equation by separation of variables. dy ху + бу — х — 6 - - dx ху — 5у ...

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Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Topic:- sequence and series

Q: If {an}1 is a convergent sequence, then {2a,}1 is also a convergent sequence. n=1 Select one: O True...

A: First is true and second is false. 

Q: In?(x) 25 log (x)

A: To find:-

Q: Question 3 Find the length of the curve with the given vector equation. r(t) = (8 - 21) i+ (4 + 6t) ...

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Q: The solution to the differential equation 1 - y = x cos(3x) is: Select one: O 1 x² cos(3x) + cx? O 3...

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Q: 6 - x 12. Solve the rational inequality x < 2x -5

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Q: Find the derivative of the function. f(e) = (3t + 18)2/3 2 f (e) = 3/3t + 18

A: Topic:- derivatives

Q: 3. S(x) = (x2/3 – 1)*

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Q: Calculate the work done by the force F(x, y) = x3yi+ (x - y)j along the parabola y= x2 from (-2, 4) ...

A: To find the workdone

Q: e3x dX be given. If U= e* + 1, then the resulting integral is J f(u) du. compute f(5). ex + 1 Let 3 ...

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Q: Find the domain of a function of the form f (x) = va – x².

A: Given function:- f(x) =√(a-x2)  To find:- Domain of given function f(x) 

Q: Let y = f (x) be a function with domain all real numbers. It is known that f ′(x) = e^x(x −2)^3(x + ...

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Q: 12X dx (x+9)0

A: We know, ∫xndx= x(n+1)/(n+1) Let I= ∫12x/(x+9)⁶ dx

Q: Find the equation of tangent line to graph at f at the given point.

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Q: 2 tan (4x – 1) – 3 cos?(4x – 1) cos (4x – 1) If we let u= 4x -1 for the integral of dx, what will be...

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Q: II. For each of the following functions, find the indicated derivative using the definition. Show so...

A: As per our guidelines we are supposed to answer only ? 3 sub- parts ( if there are multiple sub- par...

Q: III. Answer the following questions. 1. A window in the shape of a rectangle surmounted by a right t...

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Q: Find Ay and f'(x)Ax. For y = f(x) = X = - 1.6, and Ax = 0.1

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Q: ² = 4. Maximize Q = 4xy, where x and y are positive numbers such that x+y %3D y: (Type an exact answ...

A: topic - application of derivatives

Q: Q5) A) Graph the curve Y = - 2 x (x - 4)(x+ 6)(x- 2) between the value of x [0, 4], then find the ar...

A: y=-2x(x-4)(x+6)(x-2)Interval: 0, 4Y-intercept:(0, 0)X-intercept:(0, 0), (4, 0), (-6, 0), (2, 0)   Fu...

Q: dl # m S' Use Ay s f (x)Ax to find a decimal approximation of the radical expression. 27.06 What is ...

A: The objective of the question is evaluate the decimal approximation.

Q: Express the given quantity in terms of sin x and cos x. Sin (2n – x)

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Q: y y 12 12 10 8 6 4 2 21 X 2 4. 8 10 12 4 (d) Show that the slopes of the graphs of f and f are recip...

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Q: Find the maximum or minimum value of the quadratic function g(x) = 2x² + 6x + 3.

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Q: e 4x =dx Ve4x – e

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Q: cos 2X 80 dx csc (x) sec (X) CSC

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Q: B) Find the third derivative of the function: Y = + VX3 %3D

A: We have to find third derivative

Q: Q4) A) Find by using chain rule if f = ( , u=-1, x=-1 dx ++1 B) Evaluate the following integral: V2 ...

A: Given f(u)=u-1u+12   , u=1x2-1    , x=-1

Q: Given the matrix -2 3 3 6 Find the Characteristic Equation and find its solutions (aka: eigenvalues)...

A: Here we have to find the characteristic equation and eigen values of the given matrix.

Q: Q3) A) Graph the two equations and find the points in which graphs intersect x+y = 0, y= -(x-1) UNIV...

A: Given: x+y=0y=-x-12

Q: Qu 4 Using an operator , solve the following differential equations d²y dy a) dx² 10 + 25y = 0 dx

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Q: Sec2X Q1) A) Evaluate the following integral: S V1-tan2x B) Find the slope of the line tangent to th...

A: A) the given integral is sec2x/√(1-tan2x). B)y=Sin5x ; x=π/3.

Q: Find the volume V of the solid obtained by rotating the region bounded by y = sin(x?) and the x-axis...

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Q: Given: -dx. Using u-substitution and transformation of integrand, what is u and du? 3/x - 2x 3 (A) u...

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Q: 1. The graph of y=f(x) is drawn below, sketch a graph of y = s"(x).

A: Solution: According to the given graph points A(-1,3),   B(1,-3),   C(2,1) 

Q: fourth-degree polynomial with integer coefficients that has zeros 3i and –1, wit -1 a zero of multip...

A: To find a fourth‐degree polynomial with integer coefficients that has zeros 3i and -1, -1 a zero of ...

Q: b) Find the specific solution to the following 2nd order non- homogeneous differential equations d²y...

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Q: II. find an explicit solution of the given initial value problem using separation of variables. 5. x...

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Q: Question 1 For each of the following, determine whether the given SEQUENCE converges or diverges. If...

A: d) -1nen+2ne2n+ne) e2n+1en+2

Q: Find the Taylor polynomials of orders n= 0, 1,2, 3 , and 4 about =20 and then find the nth Taylor po...

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