21 x² +4x+3 4. Find lim x→1x -5x+6

Q: f(x) is a functicn given by Icosxl Assume that floe) find the pourier Series for of fe).

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Q: Using the variations of parameters method for the differential equation y" + 2y'+ y = e* In(x), we…

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Q: The graph of f is shown. y y = f(x) 6 12 18 24 Evaluate each integral by interpreting it in terms of…

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Q: Let z= y- 4a, a u'v and y-v- 3u. Compute On kum)-(1,1) -

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Q: Express the limit as a definite integral on the given interval. lim n- 00 [4(x;)³ – 4x;"]ax, [(2, 7]…

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Q: 24. Find the volume formed by rotating about the y -axis the region enclosed by: x = 9y and y3 = x…

A: Here, the curves are x=y3 & x=9y. Now, the points of intersections are at: y3=9y⇒y=0,3   because…

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Q: 1 Integrate

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Q: 5. For which values of a and b the following function is continuous at x=-2 3x + a x -2

A: A function f(x) is said to be continuous at a point x=a iff limx→a-f(x)=limx→af(x)=limx→a+f(x)…

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A: To solve the second derivative y'' of the following function and to simplify the final…

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Q: A steel girder 27 feet long is to be moved on rollers along a passageway 8 feet in width and into a…

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Q: The table above gives values of f, f'. g and g' for selected vahues (A) -14 (В) -13 (C) -2 (D) 7 (E)…

A: We will use integration by parts and will take values from table to solve this.

Q: A steel girder 27 feet long is to be moved on rollers along a passageway 8 feet in width and into a…

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Q: The following sequence (7532h n! an = e O diverges converges to e converges to 0 converges to 1

A: Given problem:-

Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: Exercise 2. Find the following limits 3x +1 1) lim 2x +5 1-3x2 3x +1 2) lim X 2x +5 3) lim x- 2x+5

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Q: The terms of a series are defined recursively by the equations az = 5 5n + 2. an. an+1 4n + 11…

A: Here, the given series has: a1=5, an+1=5n+24n+11an

Q: (c) Find marginal profit at q = 500. 10 Explain what it predicts. The total profit will increase by…

A: Apologies for the inconvenience.   #c) We have found that marginal profit at q=500 is 10.  It means…

Q: (x + y) dx dy dz =? Select one: 9. O 1 O 5 None of them

A: Topic = Integration

Q: Graph the function. Use the graph to find the indicated limit, if it exists. x20 lim f(x), fx) = -…

A: solution:-f(x)=x3 ,         x≥0-6x  ,    x<0left hand limitlimx→0-f(x)=limx→0--6x=0right hand…

Q: 8. Amanda invests some money for her retirement. The account pays 9%/a compounded quarterly. How…

A: I have stated the used formula in the solution

Q: 3. (1 + e**) + e (1-- 0 Ans. x + ye*/y = C

A: To differentiate.

Q: Find the volume by revolving the region of the curve xy = 6 from x = 2 to x = 4 about the x-axis.

A: Given xy=6        x=2 to x=4To find volume:

Q: x3 + x2 – 5x + 15 dx 5. (x2 + 5)(x² + 2x + 3)

A: Partial fraction: A complicated rational statement is decomposed into two or simpler fractions using…

Q: 1. Find y if y =x In(4x+1).

A: Use the product rule of differentiation.

Q: Find and classify all the critical points of f (x,y) = 7x – 8y + 2xy – x² + y³.

A: For critical points put partial derivate=0

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Q: Determine s) for $) = 31 + 212 1 s'() = 41 + 3 Os') = 41 + O s'() = 41 - %3D s'(t) = t+4t %3D

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Q: limn→∞ √n = ∞

A: Given :limn→∞ n

Q: Using the method of undetermined coefficients, a particular solution of the differential equation…

A: Given differential equation is y''-16y=2e4x. The characteristic equation is m2-16=0⇒m=±4. So, by the…

Q: (1) (2) (4) B" A" A" B" 90 B'

A: We will find the type of pairs of lines.

Q: For the following function f(x), find f(0) and f(2). if xs0 x2 f(x) = if 0 <x<2 x+3 if 2sxs4 4-x…

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Q: Part 2: Differentiate the following functions. Show your complete solution. 1.) (x) = (x +3x)1000…

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Q: Evaluate 3 x2 - 2y ds where C is the line segment from (3,6)to(1,-1)is C Non of the above -58.240…

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Q: Find the derivative of f(x)= x% (x% + x% +x%

A: Find the derivative

Q: The first English dictionary, prepared in 1604 by Robert Cawdrey, defined 3,000 English words. In…

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Q: The solution y, of the homogeneous differential equation y(4) + 36y" = 0 is None of them c_1+c_2…

A: We have to find solution

Q: dy Use implicit differentiation to find dx 2x - 5 3y? 2x +5 dy dx

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Q: 17. y csc(5x)

A: Differentiation

Q: Solve the differential equation dx + xdy = x?e dy. %3D

A: Given dx+xdy=x2eydyTo find solution of differential equation:

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Q: testonvergence and divergene h.

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Q: Using appropriate trigonometric substitution, dx xV4 – x² is transformed to S sin 0 d0 sec 0 d0 2 2…

A: The detailed solution is given below Thank you

Q: y=(1+2cot"x) 3 dy_ 8(1-2cot"x) dy 8(1+2cotx)° %3D dx 1-x dx 1+x? Op tion 3 Op tion 1 dy -8(1–2cot"…

A: Let's find.

Q: Assume x and y are functions of t. Evaluate dx = 9, x = 3, y = 0. for 4xe = 12 - In 729 + 6ln x,…

A: Given query is to find indicated derivative.

Q: L,x²(x³ + 8)²dx 19. Use the Fundamental Theorem of Calculus to evaluate:

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Q: Using appropriate trigonometric substitution, dx J xV1 - xV1 – x2 | is transformed to

A: Topic = Integration