Find the real solutions, if any, of the equation. Use the quadratic formula x2 + 7x + 7 = 0 of J-7 - /21 -7 +21 14 14 S-7- 77 -7 +77 2 S-7 - 21 -7 +/21 2 [7-21 7+21 2

Q: 3) A businessman ventures to put up a digital printing shop which caters to printing of t-shirts for...

A: Let the number of t-shirts that will obtain maximum gross return is = 50+x. In this case x t-shirts ...

Q: Find the limit by rewriting the fraction first. ху — у — Зх + 3 lim х - 1 (x,y)>(1,4) x+1 ху — у — 3...

A:

Q: 8. What is de x2+1

A:

Q: tan (In |4x²|) (In |(2x)^|)|+C. what is b? The integral of -dx is b In cos

A: Given: ∫tanln4x2xdx Integrate the equation we get, Consider, u=ln4x2 du=2xdx Substitute in integral ...

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 4 %3D P4(x)...

A:

Q: dx The integral k, where u= f(x) and for some constant, k. Compute 2). reduces to ex + 1 A е - 1 B n...

A:

Q: (-1)+16· 13 . 20.(7k – 8) * Use the formula for the binomial series: (1 + x)" = 1+ mx + m(m-1) m(m-1...

A: solution:-1+xm=1+mx+mm-12!x2+ ... mm-1...m-k+1k!xk              1+∑k=1∞ mm-1...m-k+1k!xk         if ...

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 5 P4(x) =

A:

Q: Problem Set A (1) For the function f(x)=1- 1x+2 find the following: (i) f(-x) (ii) f(x +k)

A:

Q: Situation 1: Find the area bounded by the curve x^2 = y + 2 and the line x + y = 0 1. Using Simpson'...

A:   A=∫-21 (-x-x2+2) dxA=[2x-x22-x33]-21 A=2(1+2)-12+2-13-83 A=112 A=5.5 square units

Q: Evaluate: lim 2 tan (r – 2) sin(x – 2)ª

A:

Q: The diagram below shows points P, Q and R. The coordinates of the points are given by P (7.),qs Q(5,...

A:

Q: 1. Consider the relation R1: R R2 such that (r1, y1)R1 (x2, y2) if and only if both points are on th...

A: We are given a relation  R1: R2  -> R2  such that any (r1, y1) , ( x2, y2) ∈ R2 are related to ea...

Q: Let 5n2 + 14n bn 3n2 an = 3n4 - 5n2 - 19' Calculate the limit. (Give an exact answer. Use symbolic n...

A:

Q: Assume that g(x) is a function given by 2.x? + 3x +2 g(x) = x² + 2 Prove that g(x) is bounded for al...

A:

Q: dy de + 2xy = 2xe-x².

A:

Q: If the solution to e2x sec2(e2x+1)dx is equal to k tan (e2x+1) + C, find the exact value of k. 1 A 2...

A: This question can be solved using the concept of integration by substitution.

Q: Why is there a need to solve for integrating factors?

A: We solve easily by using integrating factors. 

Q: The diagram below shows points P, Q and R. The coordinates of the points are given by P (2), Q(5, 6)...

A: Distance between the points P(x1,y1) and Q(x2,y2) , D = (x2-x1)2+(y2-y1)2 .

Q: Solve the components of the given equation of conic sections and sketch the graph а. х — -y2 +1 b. x...

A:

Q: Use the following results, if needed, to determine whether each series converges or diverges. If the...

A:

Q: Consider the function f :R →R given by f (x, y) = e* In(1+ y) Find Vf. What is the rate of change of...

A:

Q: Let F = %3D So Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the ...

A: Here, the given function is F=xy,5z,4y To use Stroke's theorem: ∫CF·dr=∫∫S∇×F·N^ dA And, ∇×F=ijk∂∂x∂...

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

A: Given

Q: To evaluate the possibility of using pyramid-shaped vessel, the rate of change of the dimensions wer...

A: This question can be solved by using rate of change of physical quantities.

Q: Given the differential equation y" – 2xy' + 5y = 0. Determine the first three nonzero terms in each ...

A:

Q: Question 2 12x +1 dxp. (2x- 1)2 (3x + 2)² Evaluate:

A:

Q: + oo Consider the improper integral dx . What will be an appropriate solution and answer? x2+ 2x+ 2 ...

A: We have to find solution of improper integral.

Q: Question 7 Consider the integral dx . Using u-substitution, what is the appropriate u and du? -2x 2e...

A:

Q: Compute the LU factorization of the following matrix. No row interchanges will be necessary. You can...

A:

Q: Find dy/dx 1. y = x^2(sin^−1 x)^3 2. y = e^tanh x/x^2 − sechx 3. y = tan^−1 (sechx) + sech(tan^−1...

A: We expert are following guidelines.We are supposed to do first question. We have to find dy/dx  

Q: Please see the image to see the given. thank you (a.) the critical numbers of f (b.) all relative e...

A: To find: (a.) the critical numbers of f(b.) all relative extrema of f(c.) the intervals on which f i...

Q: Consider (x8+ 8x5+ 16x2) ² -dx. Using u-sub

A: Given: - The integral is, ∫x2+1xxx8+8x5+16x22dx To find: - The values of k and n. By using u-substit...

Q: d?y Find dr2 for the functlon: .3 3x +4x y=x

A:

Q: x + px+6, x22 (b) Functions f(x)={ x-2, x<2 (4– 2x, x22 and g(x)={ are 9-x, x<2 continuous at x= 2. ...

A:

Q: 5. Find the centroid of the solid formed by revolving the area between the curves: y? = x and y = 2 ...

A:

Q: sing u-substitution, the integral Jf(x)dx reduces to a new integral J glu) du. If g(u) = , evaluate ...

A: Topic:- application of integration

Q: 2. Find the indicated limits of the following algebraic and trigonometric functions: x' -1 а. lim. -...

A:

Q: Evaluate the integral using tabular integration by parts. 4 x° V2 x + 1 dx +C

A:

Q: Find the tangent plane of the surface z = f(x, y) at (0,0, 0) in which 3y f(2, y) = || cos /3 t dt.

A:

Q: dr if r =Vs+1 and s=161-20t . dt 1. Find -

A:

Q: Use the binomial series to find the Maclaurin series for the function. f(x) =  1 (1 + x)3

A:

Q: x - 5, x21 (b) A function ƒ is defined by f(x)=. 1 x<1 Show that f is differentiable at x = 1. Hence...

A: We have to show our function is differentiable or not at x=1

Q: A consumer has utility function xy u(x, y) = x+y

A:

Q: Use any method to determine whether the series converges or diverges. (k!) Σ (6k)! O The series dive...

A:

Q: Differentiate f(æ) = 27. 1.

A:

Q: 3. S(x) = (x²/3 – 1)²

A: Given that fx=x23-12c. if f'x&gt;0 then function is increasing.if f'x&lt;0 then function is decreasi...

Q: Use the graph of the function to find the domain and range of f. (Enter your answers using interval ...

A:

Q: entences. 5k + 7k +1 3k* +8k? +9 -). az

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Evaluate

A: We will find f''(2).