2a一需

Q: The differential equation governing the decay of a certain radioactive substance through time is dq ...

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Q: Using the definition of derivative, find the derivative of f(x) = x² + 3x + 3.

A: Solution:

Q: 2. Get the general solution of the differential equation (x + 3y – 5)dx + (x + 3y + 10) dy = 0. pts)...

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Q: 2.4 Derivatives of other trigonometric functions Activity 2.4.4. Answer each of the following questi...

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Q: -0.1x dx e 1 8.

A: We use integration of e^x dx =e^x.

Q: Calculate , ešlx²+9y dx dy, where Dis the interior of the ellipse () + (5)´ < 1. (Use symbolic notat...

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Q: Use the limit process to find the area of the region between the graph of the function and the x-axi...

A: First we have to find deltax=b-a/n

Q: (d) E(-1)"2ne-i n=2 8n +5 (e) '1000n n=1

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Q: (a) f(x) = e" centered at r = 0.

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Q: m= 2-,g= 一章

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Q: A2) Find the derivative of the following functions: x² + 4 (a). f(x) x2 - 4 (b). f(x) = 2 tan-'(x) –...

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Q: h(x) = e= a + 4 – x2

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Q: s um of 5th and 9th terms of an A.P. is 72 and the sum of 7th and 12th terms is 97. Find the A.P.

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Q: Use lert and right endpoints and the given number of rectangles to find two approximations rthe area...

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Q: RFind dy/dx in terms of x and y if cos²(8y) + sin²(8y) = y+4. |

A: Given query is to find the derivative of the given expression. Pp

Q: The amount, A mg, of caffeine in the body t hours after drinking a cup of coffee can be approximated...

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Q: M. 33. 5k

A: 33.   The given series is ∑k=4∞15k

Q: Evaluate :[x' {(1+x°)'dx is (1+x) dx

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Q: Consider the function f(x)=−2x^3+42x^2−240x+9. This function has two critical numbers A<B: A= ? and ...

A: We use derivative of function to find the required solution.

Q: DETER Derer mine the fieSt os: mine the キ)12ST oこ: derivative F6) = aresee(3x) %3D

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Q: Find the 7th term of the geometric sequence 2, -6, 18, ...

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Q: (e) In electrical circuits, Ohm's law can be mathematically modeled as /=V/R, whereas / is the curre...

A: To find the rate of change of current with time 

Q: 1 57. > Σ (k+6)(k+ 7) k=1

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Q: A population of bacteria is growing according to the equation P(t) = 550e0.224, Estimate when the po...

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Q: EXAMPLE 3 Find dx. 3 - 3x SOLUTION Let u = 3 - 3x2. Then du = dx, so x dx = du and dx 3 - 3x2 u-1/2 ...

A: Given: ∫x3-3x2dx

Q: Consider a solid cone with radius a and height h. How far from the vertex is its center of mass? For...

A: Given the radius of the cone is a Height of the cone is h Let us solve the problem using centre of m...

Q: lim x3 -1 is x-1- x -1 А. — 3 B. no limit C. 3 D. undefined Е. О

A: topic - limits

Q: Speedometer readings for a vehicle (in motion) at 3- second intervals are given in the table. v (ft/...

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Q: lim 7-4x-x4 2(x-2) lim 2x+1 人Y8 lim (Jx4-2x)

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Q: PARTIAL FRACTION DECOMPOSITION. Use partial fraction decomposition to evaluate the indef- inite inte...

A: Here we need to solve the given indefinite integral using integration py partial fraction decomposit...

Q: Let A(x) = f(t)dt, with f(x) shown in the graph below.

A: Given that: Graph of f(x)

Q: 8m3 - 27 2 lim 2m - 3 m- 2

A: a³ – b³ = (a – b)(a² + ab + b²)

Q: Find a Power series representation for the function f(x)=In(5-x); And find the radius of convergence...

A: First we have to convert given function into one of the standard forms

Q: (10) Use Cramer's rule to solve the following linear system of equations: x + 2y = 2 %3D x + y = 0

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Q: Find the equation of the vertical asymptote and the equation of the slant asymptote of the rational ...

A: Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of t...

Q: PARTIAL FRACTION DECOMPOSITION - SET UP For each of the following rational functions, choose the cor...

A: Given the functions 

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 2.2 ft^3/min. How ra...

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Q: If x^2+y^2=25 and dx/dt=6, find dy/dt when y is positive and (a) x=0: x=1 x=4

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Q: 7topic: implicit differentiation

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Q: Use Linear Approximation to estimate Aƒ = f(3.02) – f(3) for f(x) = sin(). (Use decimal notation. Gi...

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Q: Question 4 and 9 please

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Q: Suppose the population f (t) of a given species grows exponentially, so that f (t) = f (0)ekt for so...

A: topic - exponential function

Q: 2.) xe" dx 8.

A: Given query is to find integral converges or diverges.

Q: dy 3. x =y+y³cosx dx

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Q: (-1)") 55. 2"

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Q: Sketch the triangle with vertices O,P = (4,0, 2) and Q = (4, 3,0) and compute its area products. usi...

A: To find the area of triangle

Q: lim [(cos(rt) + 3) i +²j+ (3° +3) k] = t→0 lim [e'i+ 3r° j+ e'k] = t→1 lim [sin(3rt) i + 3f| = t→-2

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Q: Find f[fp Vx2 + y2 + z² dV, where D is the sphere of radius a centered at the origin.

A: We need to find the integral:∫∫∫Dx2+y2+z2dVwhere D is the sphere of radius a centered at the origin....

Q: 200 2.0 Determine the inverse Laplace transform of s2-50s+10625

A: According to Bartleby guidelines, I can solve only one question at a time. If you want solution of o...