For each natural number n, the expression 2* – 7n - 1 is divisible by

Q: Evaluate the limit In(x) lim x+1 x- 15x+ 14

A: Given,  limx→1ln(x)x2-15x+14

Q: 1. Consider the lines x = -1+ 2s by:- = and t2: y=s x – 5 l1 : 3 – z %3D 4 z = 5+ s а. Find two unit…

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Q: A. For each of the following functions z, find and dx ду 1. z= sin3x cos4y 2. z = tan- 1 (2) 3. yz +…

A: 1). Given: z=sin3xcos4y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x…

Q: dy x- +9- tan-1x = 0 dx

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Q: hi, in no.1, instead of y=x2 + 2, you entered y=x2-2, so is the graph right? the point is supposed…

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Q: 1 1. lim x-0+x e*

A: Given: limx→0+1x-1ex-1   So, simply we can write as; limx→0+1x-1ex-1=limx→0+ex-1-xxex-1

Q: The radius of a circle is found to be 7 cm in length with a possible error of no more than 0.04 cm.…

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Q: 4. Determine the equation of the plane passing through the point (1,-4, 3) and parallel to the plane…

A: Explanation of the answer is as follows

Q: [6]. Consider the following set of parametric equations: x = r° - 3t y = 312 – 9 On which intervals…

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Q: Evaluate the limit x2+ 19x-48 lim x²+9x+112 X- - 16 X a. 13 23 O b. 19 23 O C. 00 O d. None of…

A: The detailed solution is given below Thank you

Q: d of Variation of Parameters: [D² - 8D + 16]y = e4%sec2 %3D

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Q: Find the inverse transform, indicating the method used and showing the details: 2s - 10 -5s 1. s3 3s…

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Q: ) Eliminate the arbitrary umstants of y= C, + C2 e ** + C3 e 3x

A: The given equation is y=c1+c2e2x+c3e-3x. We have to eliminate arbitrary constants c1, c2, c3. Since…

Q: 4 -2 3 1 3 2 15) - 2 1 Ans. -3, 2 ; 5, 0 1 2 2

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Q: 4. State whether the given measurements determine zero, one, or two triangles. A = 43° a = 8 b= 10…

A: We will use Sine /Cosine rule to find the triangle.

Q: Expand and simplifyW – 35) · (5 + 2w)

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Q: S 23x26 ++16 dx

A: Here we have to integrate the given Integral.

Q: olve the triangle. 95 a-6 b- 4 Select the correct choice below and, if necessary, fill in the answer…

A: Here is the solution

Q: (x, y) = (1, –1) { 1 Show that the function f defined by f(x, y) x2 + y (x, y) # (1, –1) x + y is…

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Q: If f'(2) = 5 then [4f(x) – x³]x=2 %3D dx Select one: O 32 O 8 O 28 O 20 O none

A: Given f'(2)=5To find ddx[4fx-x3]x=2

Q: VII. Use Lagrange Multipliers to solve the following: Maximize f(x, Y, z) = 4x + 2y + z %3D subject…

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Q: 10 Find the derivative f' (0) of f(x) = at х+4 O using the laws of differentiation.

A: f(x)=10x+4DIfferentiate w.r.t.xf'(x)=ddx(10x+4)Take constant outf'(x)=10ddx(1x+4)f'(x)=10ddx(x+4)-1…

Q: Write down the gradient of the straight line represented by the equation y = −0.05t + 47. What does…

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Q: 2. The number, N, of bacteria in a culture at time t, in hours, is N(t) = 1000[30 + e a. What is the…

A: Topic:- exponential function  Note:- as per our guideline if more than three subparts posted than…

Q: f (x+h)-(f(x) 7. In finding the limits of the difference quotient ,on what value does k approach? a)…

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Q: Evaluate each limit: x +x-30 a) lim x-3 x-6x+5 3-1-4x b) lim X-2 x+2 x+3 c) lim x→-3 Vx-5+2

A: Limit

Q: A particle is moving along a horizontal path which starts at a distance of 5 ft to the right of a…

A: We need to determine if the particles collide or not.

Q: Convert to degrees and write it as the least possible positive coterminal angle. a. -220° b. 120° C.…

A: We have to find the angle

Q: Use Method of Variation of Parameters: [D2 - 8D + 16]y = e4Xsec2x %3|

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Q: 3 Use the linear approximation to estimate Af = f(3.1) – f(3) for f(x) = I+x (Use decimal notation.…

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Q: f'(x)=-+e2* +x² and S(1) =. Find f(x) Given %3D

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Q: 2. Which is the interpretation of the statement lim f(x) =L? i. For all x values close to c, but not…

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Q: sin x S + 3x)dx 1. cos x dx 8 sin?x cos²x 4. 了 1 2. 了 dx 1-cos x 5. J sec x(sec x – tan x) dx 2 secx…

A: These all are solved by the help of standard trigonometric Antiderivative.

Q: 2) Eliminate the arbitrary enstant, 4 y= x*+ Cix + Cz e-X

A: Given problem:- Eliminate the arbitrary constants. of y= x² + C₁x + C₂ e-x

Q: 2. xy dx dy

A: While integrating wrt 'x' we will keep 'y' as constant. While integrating wrt 'y' we will keep 'x'…

Q: Find Valke of nhegal Sxdx X dx

A: To evaluate the given integral

Q: Find the first three nonzero terms of the Maclaurin expansion of the function. f(x) = 8 cos TX ...…

A: The Maclaurin series is given by  f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: 2+ In² 1 dx. 4. Evaluate the integral x – x ln x (a) 3 ln |In r – 1| + 2(ln x – 1) + (In x – 1)2 +C…

A: To find out the integration.

Q: .What is the limit of the sequence an = [(n2 - 1)/(n2 + 1)]n

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Q: 1 X• In( coS lim (* - In(cos )) x00

A: Given

Q: d radius of the

A: If r = A cosθ + B sinθthen Centre is A2 , B2 and radius is A2 + B22

Q: Se6m sin m dm Integration by Parts m3+4m Algebraic Substitution (1-m*)2

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Q: 7. Find the volume of the solid obtained by rotating the region bounded by and r = 0 about the…

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Q: Evaluate the guen -x>·dR,where conGists of the upper past F the cuafe x ty"=1 from "(-1,0) parabala.…

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Q: dx (9 – 4.x²)³/2 2,3/2

A: Use substitutions to make it more simple

Q: 1. dr COS 2. sin

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: ds Find dt 1+ tan t S= 1- tant

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Q: II. Find the area bounded by each of the following curves. Show your complete solution. Write your…

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Volume of Solid Revolution(Circular Disk/ Washer Method) Find the volume of the solid generated by…

A: Given problem:- Find the volume of the solid generated by revolving the area bounded by the given…

Q: Evaluate the limit In(x) lim x+1 x2 - 19x+ 18 a. 1 19 O b. 19 C. 1 17 O d. None of these. е. —17

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