Use the Binomial Theorem to write the expansion of the expression. (r + 3s)3

Q: Evaluate the limit. 10 lim x→1 х — 1 х2 + 8х — 9 Give your answer in exact form. If the limit does…

A: We have to check limit exist or doesn't exist

Q: Identify the interval of convergence. (Enter your answer using interval notation.)

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Q: Question Specify which of the following sequences converge en n+V5 an =5- %3D n2 Cn = an and Cn the…

A: If limn→∞an  exists and is finite the then sequence an is converges.

Q: Use a triple integral to find the volume of the given solid. The solid bounded by the parabolic…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t? + 4 1 lim 5t2 + 6 7t (?,?)

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Q: E-10: Let f(x) be a non-constant polynomial satisfying the relation f(x).f (y)= f(x)+f(y)+f(xy)-2,…

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Q: Find u + v, u - v, and 4u 5v. Then sketch each resultant vector. - u = (-4, 2), v = (3, -6) %3D (a)…

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Q: Evaluate the integral. n/2 5 cos?0 de

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Q: Evaluate the double integral over the rectangular region R. y'dA; R = {(x, y): -1sxs1, - 8 <ys 8} |…

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Q: Let f(x) = 10x + ax² + e2×. Compute f()(x). %3D (Use symbolic notation and fractions where needed.)…

A: We need to find the 7th order derivative of the function f(x) given by

Q: Where is each function continuous? (b) f(z) = sin (1-r) I+3 (c) f(r)= In (d) f(r) = 12+5r +6

A: Topic:- function

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

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Q: Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs…

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Q: Evaluate the double integral over the rectangular region R. || xV16 – x*dA; R = {(x. y): 0 < x < 4,…

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Q: Q1. Answer the following question in short: 1.1 Simplified form of v-25 + 3v-4 + 2v-9 is 1.2 The…

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Q: Given the following functions: f(x) = cos(x) g(x) = x7 + 1 d d Find f(g(x)) and g(f(x)). (Use…

A: Given the following functions: fx=cosxgx=x17+1To find ddxfgx and ddxgfx.

Q: Find the exact values of the remaining trigonometric functions of theta satisfying the given…

A: Follow the procedure given below.

Q: Find the values of c guaranteed by the Mean Value Theorem (MVT) for f(x) 1 ax +7 over the interval…

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Q: A one-product company finds that its profit, P, in millions of dollars, is given by the following…

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Q: Find the solution of the following BVP given that y(0)=2 and y(1)=0. d’y_12dy. dx +36y = 0 dx

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Q: 3 The series E converges if n=2 (n+ 1)P (n – 1)ª (a) p+q1 (c) p+q=1 (a) p+q=2 (e) -1<p+q<1

A: Solve the following

Q: Find the points on the curve where the tangent is horizontal or vertical. You may want to use a…

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Q: x-3 j. lim cose sine- sin 00 02

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Q: 2x and y 4x?. Sketch the region enclosed by y Find the area of the region.

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Q: 4 The net signed area in the above graph can be written as (mæ + b)dx, where c = d and b = = U

A: The net signed area in the above graph can be written as ∫cdmx+b dx, where c=?,  d=?m=?, and b=?

Q: Indicate whether the following statement is true or false. The function f (x) = |x| is continuous at…

A: Solve the following

Q: Estimate the area under the graph of f(x) = 36 – x² over the interval [ – 6, 4] using eight…

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Q: 4 – X - 2 2 sin(x) |dx V 1 + x

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Q: 3600 The function s(x) = = 3600(60 +x)' gives a person's average speed in miles per hour if he or…

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Q: Find the volume of the solid that results when the shaded region is 3 revolved about the indicated…

A: The region is bounded by y=3x2 and y=3x3 from x=0 to x=1 revolved about x-axis.

Q: 1. Set up the following improper integrals by definition. sin(x) dx 22 — За — 4 а. xe dx с. 4 et b.…

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Q: Evaluate the line integral (4х + 5у)dx + (За — 6у)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: 7.5x A sketch of the region enclosed by y = x and y follows. x2 + 1 -3 -2 -3 Area of the region =

A: Let's find.

Q: k lim (1+†) k→∞ k

A: We have to find limit

Q: Evaluate the iterated integral. 5 cos(r + y +:) dz dx dy

A: We know that integration of sinx is -cosx + c  and integration of cosx is sinx + c.       Here i…

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

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Q: 12. Find an equation for the tangent plane to the surface given by 2xy = 2z2 - ryz at the point…

A: Use tangent plane formula

Q: Find a power series for the function, centered at c. 1 h(x) 1 C = 0 8x' h(x) = n = 0 Determine the…

A: We have to find the power series and interval of convergence.

Q: dx a sin x+b cos x

A: Given problem:-

Q: Find an equation of a line through the point (-1,3) making an angle of 45 degrees with the line…

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Q: Find the Laplace transform of: f (t) = v1+ sin t + (7t)14 + t² sin 2t

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Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: S 4x53x dx 3.)

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Q: We know that y dy? arctan (e*+1) so whats the value for dx 1 a) e2a+2 +1 1 Ob) els+1)* +1 Need This…

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Q: Evaluate the indefinite integral. 8 + x*dx + C

A: topic- indefinite integral

Q: first octant 2 4- x+y dy dx -

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Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

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Q: 0, 1, 2, 3, and 4 about x = xo Find the Taylor polynomials of orders n = and then find the nth…

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Q: 35. If y=3x^2-x+1, find the point x at which dy/dx assume its mean value in the interval x=2 and…

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Q: Let f(x) = 10x6 + xx² + e2x. Compute f()(x). (Use symbolic notation and fractions where needed.)…

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