cos² (3n+7 {a,} = 3n² +1

Q: The area under the graph of f(x) = 3x2 between x = 2 andx = k is 504, where k > 2. Find the value of…

A: Given

Q: 1. Find the absolute extrema, if any, of the following functions on the given interval. (a) f(x) = 4…

A: Given:     a) fx=4-3x ; (-1,2]           dydx=ddx4-3x                   f'x=-3   There in no…

Q: Use the transformation u = 4x + 3y, v = x + 3y to evaluate the given integral for the 4 4 region R…

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Q: Find a formula for the nth term of the sequence 1, - 4, 9, – 16, 25, ..

A: We can find the nth term of the sequence. We notice pattern of the sequence.

Q: Differentiate each function by applying chain rule. Match each item to a choice: y = x(x² + 3)² y =…

A: We have to differentiate following functions using chain rule: y= x(x2+3) 2 y= (4x-10) 4 y=…

Q: 3. xy' =y-xe/x ANS y =-x

A: To find out the solution of the differential equation.

Q: Suppose that for a company manufacturing bluetooth and wireless headsets, the cost and revenue…

A: Let's find.

Q: Find the equation for the line tangent to the curve 2e"y = x +y at the point (2, 0). Explain your…

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Q: a. (csc 0)(1+ sin² 0 + sin 0 cot? 0) d0 5.

A: We will solve the integration

Q: 12 dx Jx3 – 3x2

A:

Q: Consider f(x) = cos (x) ln(x +2). a. Find the local linear approximation of f(x) at xo = 0. (In 2 z…

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Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

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Q: Let f(x) = ax* + bx² + 50. Determine the values of a and b so that f(x) has a point of inflection at…

A: We have to find value of a and b

Q: Use the substitution u = 6x? + 1 to convert the integral fo xeoz+1 dx to an integral of the form L…

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Q: Find the general equation of the tangent plane to the surface x2 + y2 −2xy −x + 3yz = −4 at the…

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Q: The graph of a function f is given below. According to the graph, the derivative of the function…

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Q: Find the Taylor series generated by f at x = a. 1 a = 4 f(x)= x

A: We are asked to find taylors series of the function

Q: Find a formula for the nth term of the sequence. - 1, 4, - 9, 16, -25, .. Determine the sequence's…

A:

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: As we know the surface area of the cube is; S=6a2                            ...(1) Where 'a' is the…

Q: 2у — 4 dy 2 + 49 с.

A: To evaluate: I=∫2y-4y2y+2dy=-∫4y-2y2y+2dy=-∫22y-2y2y+2dy=-∫2y-12y+22ydy=-1ln 2∫2y-12y+22yln 2dy

Q: .9

A:

Q: 4 y = ,x = 1,x = 4, and y = 0 is revolved about the y – axis. (Answer: 24n c. u.)

A: This question is based on finding volume of solid.

Q: Vhich of the following are possible f '(x) for a function f(x) that is decreasing for every x > 5?…

A: We are asked to find which is decreasing

Q: x²+3 Suppose y = and x = sin (u)ln (u) a. Determine dy using the first principles definition of a…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: sin(x²) Evaluate lim 140- e2r – 2x – 1

A: Topic = Limits

Q: Q3: A. By power series, prove that: d Cosx = -sinx dx B. Find the value of x for which Inx + (Inx)²…

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Q: 2. If the acceleration function of a certain particle is given by a(t) the velocity function…

A: We know that if we integrate the acceleration function then we get the velocity function . we used…

Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

A: Given: We have the local maximum at the point (7, -6). So, we must have f'(7)=0. Here, f'(x) =…

Q: derivative(y

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Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 3…

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Q: Question 9 Let y = tan e find the differential dy of the function. O dy = e (r – 1) sec e- da O dy =…

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Q: V. ASSESSMENT (Time Frame: (Learning Activity Sheets for Enrichment, Remediation, or Assessment to…

A: Given

Q: x2 Consider the function f(x) = - x2 -1" (a) Find the intercepts of the graph of f (if any). (b)…

A:

Q: 1. Evaluate the following integrals. sc 8)(1+ sin² 0 + sin 0 cot? 0) d0 a.

A: Given: I=∫cscθ1+sin2θ+sinθcot2θdθ     Use the trigonometric identity; 1). sinx=1cscx 2).…

Q: x² – 4 For the function f(x) =- x' +3x – 4 a) Find the equation of the vertical asymptote(s) b)…

A: Solution is here

Q: B- Find the length of the curve given by the position vector r=, =r'i+(1+(1/3)x')j+(1-(1/3)')k for

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Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series…

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Q: Q1: To integratef 6x + 8 dx we substitute a)x = sec 0 + 3 b) x = tan 0 + 3 c)x sec 0-3 d) x 3sec 0…

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Q: Use the Table of Laplace Transform to find the Laplace Transform of the given function. I. d. sin3t…

A: Laplace transform

Q: Find the derivative of the function at Pn in the direction of A. f(x.y.z) = xy + yz + zx, Po(2, - 2,…

A: The  derivative of f at the given point is given below.

Q: 00 Write the Taylor series for f(x) = e* about x = Σ- 3)". 3 as n=0 Find the first five…

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Q: Are the Following Vectors Linearly Dependent or Independent? 3) (0,1,0), (2,1,0), (3,4,7) Ans.…

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Q: parhod derivohve of 4,5 43 6- 13

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Q: Let B be the sphere x2 + y? + z? = 1. The volume of the portion of B contained in the first octant…

A: Given : B be the sphere x2+y2+z2=1

Q: Suppose f(x) is positive, continuous, and f'(x) < 0 for all æ in [ – 8, 4], and| f(x)dx = 76 and L…

A: Concept: Mean value theorem: The mean value theorem states that if a function f is continuous over…

Q: II. Find the Inverse Laplace of the following 2s-9 d. s2 +2 1 е. (s²+1)(s²+4s+8)

A: We have to find the inverse laplace transform.

Q: In a race, Molly starts running from rest at a constant acceleration of 3 m/s². She is running in a…

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Q: 00 4n 6(-7)"x

A: