B. Solve the following problems using differentials and linear approximations. Show complete solutions 3. The radius of a sphere is increased from 20 cm to 20.2 cm. Estimate the change in volume.

Q: Consider the parametric curve given below. = 2t3 - 15t2 +36t y = 2t3 + 18t2 + 48t

A: Tangent is horizontal at the where slope is zero ie.  dydx=0

Q: Calculate the higher derivative. (Use symbolic notation and fractions where needed.) d? 8 cos (1) =…

A: To find,  d2 dt28 cos2(t)

Q: 36 – x2 – y? and S2 be t Let Si be the hemisphere with Cartesian equation z = 6 – upper nappe of the…

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Q: Determine whether the sequence is convergent or divergent. If it converges, find the limit. S(3(n –…

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Q: Calculate the first five derivatives of f(x) = – sin(x). Then determine f(8) and f(9). (Use symbolic…

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Q: ||r'(t) × r"(t)|| ||r'(t)||³ Use the formula k(t) = to find «(t). r(t) = e""i+ e'j K(t) =

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: r(t)=cos(πt)i-ln(t)j+t-12kDomaincos function takes all values  ie  -∞,∞logarithmic function takes…

Q: Dx) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and…

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Q: Q3) Evaluate triple integral f, (x2 -y²)dz dx dy.

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Q: Question 1 Area bounded by the curves y=e", y=e", x=0 and x=In2 A 604/9 B 502/9 304/7 304/14

A: Ara of the above bounded curve is given by

Q: Evaluate the limit sin 3x lim 9x

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Q: 6 sin z Let f(r) = 6 sin z + 2 coS T Then f'(x) = The equation of the tangent line to y = f(z) at a…

A: Given query is to find the derivative of the function.

Q: x Algebra In Exercises 19 and 20, for what values of x and y are the triangles congruent by HL? 20.…

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Q: Starting at age35 ​, you deposit​ $2000 a year into an IRA account for retirement.  Treat the yearly…

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Q: Evaluate the integral. HINT: [Use a shortcut.] e 8x - 1 dx

A: Using substitution ,

Q: Find the limit. lim (t i - 7 j+1² k) t-5 lim (t i- 7j+? k) = i i+ i j+ i k

A: To find the limit of the given vector valued function.

Q: {(1-9*"} bn a,b e R n

A:

Q: Find fr(x, y) and fy(x, y) given f(x, y) = tan x· cos os(x² – y?).

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Q: S cos³ 3x dx со

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Q: am dA y² dx + x² dy = / / ( - əx ду for the given path. hC: rectangle with vertices (0, 0), (2, 0),…

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Q: Find the arc length L of the graph of r(t). 1 r(1) = r} i + t j+ Vor² 2<t< 5 L =

A: We need to find arc length.

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) (t) = (e-e 2 %3D L{f{t)}…

A:

Q: Find the minimum and maximum values of the function y = x-1 on the interval [1,6] by comparing…

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Q: Calculate the derivative (implicit derivative): y + 19xy = Cos(7x – 5y) %3D |

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Q: Example: Find C² sint]? Solution:

A: To solve the following problem

Q: d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Let C1 be the curve with parametric equations x = Cos t, y = sin t – t, where t e [0, ). (a) Find…

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Q: Determine the value of c for which lim (1 + 2,5n = ell n-00 сп

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Q: Find the area enclosed by the curves y = y = 2 1- 9x2 2n B 3 D 6. [+

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Q: If a club consists of 13 ​members, how many different arrangements of​ president, vice-president,…

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Q: 13. Find the mass of a thin funnel in the shape of a cone z = x² + y²,1<z< 4, if its density…

A: It is given that, the equation of a cone is z=x2+y2,1≤z≤4 and the density function is δx,y,z=10-z.…

Q: What is the difference between contanity? Unforly contanity ?

A: This question is from real analysis &amp; our topic is uniform continuity .

Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i %3D Duf = i

A:

Q: Draw the Root Locus curve for the equation s (s + 2) (s + 3) + K (s +1) = 0.

A: We have to draw the root locus curve.

Q: Evaluate the integral 24 11) dx, by making the appropriate substitution: u = Ja* (2* – 11)*“dz =

A: ∫ un du =un+1n+1+C

Q: actorise the polynomial 2x3 – 3ix² + 2x – 3i. Show all working.

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Q: 1. Use a suitable substitution to evaluate , (G) dx. Give you answer correct to at least 2 decimal…

A: Substitution is done for the function whose derivative is present in the numerator.

Q: Evaluate the definite integral. NOTE: Enter the exact answer. |ti + t*|dt (25;² + 1) – 1 3j2

A: The given integral,                        ∫05ti+t2jdt

Q: Lnx sin 2x dx

A: Use the properties of definite integral and solve the question.

Q: Find f'(÷) for f(x) = 2 sin z cos x

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Q: Q11. Suppose z = f(x, y), x = g(t), and y = h(t) satisfy: h(7) = -2 h'(7) = 1 f-(2, –2) = 2 fy(2,…

A: Suppose z=fx, y, x=gt, and y=ht satisfy: g7=2, h7=-2, fx2, -2=2g'7=-3, h'7=1, fy2, -2=0By using the…

Q: | (2x - y) dx + (x + 9y) dy. Ic Evaluate C: x-axis from (0, 0) to (0, -9) and (0, -9) to (5, -9)

A: We can solve as follows

Q: Find the consumers' surplus at a price level of p= $160 for the price-demand equation below. p =…

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Q: Find the producers' surplus at a price level of p = $59 for the price-supply equation below. p= S(x)…

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Q: Use De Moivre's theorem to solve for z given z = 3 – 2i. Write your answers in rectangular form. Use…

A: Given: z5 = 3-2iz   = 3-2i15                                     1-------------------De-Moivre's…

Q: Consider the function f(x) = -4xi + V24 -x on the interval [7, 27]. Find the absolute extrema for…

A: We want to find absolute maximum and minimum.

Q: Determine the inverse Laplace transform of the given function 25 L-1 [s²(s² + 4s + 5)]

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Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for tN 0. Then the integral L{f{t)}…

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Q: which of the following option(s) contain only values of x for which the power series converges? Mark…

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Q: 10 9. Consider the function f(x) %3D Let F(r) be the antiderivative of f(z) with F(1) - 0. Then F(x)

A: