Derivatives: using (4 step rule). 1. q(t)=10 + 5t – 1? 2. s(x)= 3-x ,2 4. f(x)=sin3xcos 3x 5. f(x)=x² cos(x² +1)

Q: 4. S ( 12 x³ + 15 x - 20 ) dx 5. S 10 x2/5 dx 6. § 3 ³V x8 dx 7. S ( 8 + 2 dx x3 x4. 8. S ( 2x³ -…

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Q: - 2 Evaluatelim x- 8x2-7x-8 O 1/9 O 27 O NONE OF THESE 1/12

A: To evaluate: limx→8x3-2x2-7x-8

Q: 1. If f(x)=1/x, which of the following is the simplified form of the difference quotient? * -h -1…

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Q: Solve the given differential equation by separation of variables. dy - ху + 4y — х - 4 xp ху — 5у +…

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Q: (a) Estimate the area under the graph of f(x) = 2 + 4x2 from x = -1 to x = 2 using three rectangles…

A: The given function is: f(x)=2+4x2; x=-1 to x=2

Q: If A and B are similar, then there exists a matrix P such that Bk = P-1AKP., Use this fact to find…

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Q: Solve the following and show the complete solution. Find D,f at P: f(x,y) = sin(8x – 5y); P(5,8)); u…

A: Given,            fx,y=sin8x-5y ; P5,8 ; u=35i-45jTo find : The directional derivative, Duf at P.

Q: 9) Given the function f(x)=-x+4 , find the net signed area between f (x) and the x-axis over the…

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Q: 15.lf f(x)=Vx f(x)-f(16) The lim x→16 x-16

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Q: Y thenumber of Limits of. E -63? gontric k series Skz Ak=7 B に2 6 Ok26 No if the above.

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Q: 5x2 + x + 16 dx x3 + 4x 9)

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Q: Prove that you Can use the integral teSt on the Series which is the Sum to infinity of the terms a…

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Q: 里() t² + 5 1 lim t一+05t2 +6'2t (?, ?)

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Q: y(x)=asin2x+bcos2x, where a and b are arbitrary constants, is solution of the differential equation…

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Q: Find the length of arc of the given curve.

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Q: 1) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 1.1., # 37 or from your…

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Q: The world population at the beginning of 1990 was 5.3 bilion. Assume that the population continues…

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Q: Find the area of the region between the graphs of f (x) = 3x3 – x² – 10x and g(x) = -x2 + 2.x, %3D -…

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Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). f(x) = 5 sin (4x³) If…

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Q: -1 8 - 2 Use this procedure to find the inverse of A =| -6 49 -4 34 -5

A: We can solve this as follows:

Q: 11T If 0 = then 6 sin(0) = cos(0) Give exact values. No decimals allowed!

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) = V…

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Q: Find T(t) and N(t) at the given point. r(t) = (t² – 8)i + tj; t= 8 %3D T(8) = | %3D N(8) =

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Q: 1. For each of the following, state whether the equation is ordinary or partial, linear or…

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Q: List the first 5 terms of the sequence. 32 + 3n3 22 1 (а) ап — 3n3 n2 + 3n3 4 (b) (-2)n+1 + 3n 3n3…

A: a)an=13n3+223n3+323n3+......+n23n3b)4-2n+1+3nn=1∞

Q: ||F(t) × r"(})| ||r(t)||° Use the formula k(t) = to find k(t). r(t) = 11 cos(t)i+11 sin(t)j + 6tk

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Q: 17. SHOW ALL WORK Use De Moivre's Theorem to evaluate the expression. Write the result in standard…

A: Given,              1-i4To find : Use De Moivre's theorem to evaluate the expression.We know that,…

Q: llowing series determine if the series converges or diverges cence or divergence. (e) Alternating…

A: We have to check the given series is converges or diverges according to the given information

Q: Use the formula k(t) ||r'(t) × r"(t)|| to find k(t). ||r(t)| r(t) = 11 cos(t)i+ 11 sin(t)j + 6tk

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Q: Find the component form and magnitude of the vector v with the given initial and terminal points.…

A: Given,  Initial point: (3,2,0)  Terminal point: (4,1,8)

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (9, 5)…

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Q: 6) (7 tarr-3/2 x secdx dx

A: Here we have to solve the given integration.

Q: The diagram at the right represents the height of a blimp flying over a football stadium. Find the…

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Q: 2. t23* dt

A: The given problem is solved below in detail.

Q: Solve the initial value problem. 2x(y + 1)dx – ydy = 0, where x = 0 and y = -2. %3D %3D

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 7 Ex + 3y +z = 8 Find the normal vector, n,,…

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Q: 2- 4 The graph of f is shown in the figure above. If , f(x)dx- 2.3 and F'(x) f (x), then F(3)-F(0)=

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Q: 4x? ds where Cis the portion of the curve y y° 1 =- from Evaluate the line integral (1,1) to (2,4).

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction V -6…

A: This is a problem related to vector calculation. Based on the general formula we will answer the…

Q: Find the mass and center of mass of the lamina bounded by the graphs of the given equations with a…

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Q: For each of the following series determine if the series converges c for series convergence or…

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Q: Determine whether the following series converges or diverges. Σ 5n2 +5 n=1

A: We can solve the given problem as follows:

Q: An integral is given that can be evaluated using integration by parts. Write expressions for u, du,…

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Q: x2 – 25 dx 7) S-

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: Q1. Choose the correct option: a) Let f(x) = |x]. Then at x = 0, the function f(x) is: %3D (A)…

A: This is a problem of limit and continuity parts. Please find the solution below.

Q: nd the average value of the function over the given interval. (Round your answer to three decimal…

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Q: I = -2+3s z + 4 1. Consider the lines defined by the equations l : x – 2 = y – 1= and l2 : y = -1+ s…

A: Given:  l1= x-2 = y-1 = -z+42=tl2= x+23 = y+1 = z-2-4=s

Q: Given the series: 1 1+ - 6. 1 1 + ... 36 216 does this series converge or diverge? O diverges…

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Q: The other type of question in chapter 7 is solving trigonometric equation. We will not be practicing…

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