SOLVE STEP BY STEP IN MAT Determine the equations of the lines tangent and normal to the curve defined by x² + 4xy + y² = 13 at the point (2,1).

Q: 8. For the angles a and b in the figures below, find the exact answer for cos(b-a), without using a…

A:

Q: The following subsets A, B, and C of RX R are relations on R. Sketch the set. (i) B = {(x, y): [x] +…

A:

Q: Find a matrix P such PTAP orthogonally diagonalizes A. A = -2 24 2-24 44 4 st

A: As per the question we are given a 3×3 symmetric matrix A and we have to find an orthogonal matrix P…

Q: Show that any sequence of positive real numbers either has a subsequence that converges, or else a…

A: Let (an) be a sequence of positive real numbers.  Case 1: Let (an) is bounded above.  Since (an) be…

Q: 4 [5], 9 (a) Write b as a linear combination of a₁ and a2. Let al b a2 = -8 7 and T(a₂) and b = 2…

A: See below for the complete solution -:

Q: 2. Determine half range Fourier sine series for f(x)=x(n-x) in 0<x< T hence deduce +3/3+²/2+ π³/3².

A: Since you haveposted multiple questions, we will solve the first question for you. If you want any…

Q: If f, g, and h are differentiable functions of x and 8 h (xg)' (xh)' (x²g)" (x²h)" A(x) = (xf)'…

A:

Q: If A 0 " P= [13] AP= PA, then what is A¹⁰ ?

A: Given: A=5-230, P=1213 To find: A10.

Q: Find the Kernel of the following linear transformation. Also find the Ker(T). (i) T: P3 → P2, where…

A:

Q: B. f(t) = t³ >= {₁² 0 0 sit 2

A:

Q: x³ + y³, y³ + z nt) Calculate the flux of the given vector field F = e S where S is the sphere…

A:

Q: Let S be a linear transformation from R³ to R² with associated matrix A = - 2 0 -1 2 2 1 2 Let T be…

A:

Q: You need to provide a clear and detailed solution for the following Questions: Question . Let W be…

A: Basis: A set of vectors S is said to be a basis of the vector space V if it is linearly independent…

Q: For each of the following series, determine whether the series converges, diverges to ±∞, or…

A: The given series are: i. ∑sin23n+22n2-3 ii. ∑1n-2π iii. ∑n+1n3+2 We have to determine whether the…

Q: Find the volume of the solid bounded by the cylinders x² + z² = 1 and y² + z² = 1.

A: The given problem is to find the volume of the solid bounded by the given cylinders x2+z2=1 and…

Q: Solve graphically (find the maximum and minimum of the objective function z); all variables are…

A:

Q: ܐܠܕ 1 x y3+1 dydx

A: We need evaluate the integral: ∫04∫x2 1y3+1dydx . Plot the domain of integration and switch the…

Q: Alte

A:

Q: se the Divergence Test to determine whether the following series diverges or state that the test is…

A:

Q: A window has the shape of á parabola above and a circular arc below. Find the area of the window…

A: To find: The distance from the x-axis to the top of the circle. Write the equation of the circle.…

Q: 15. Kitchen's Contracting determines that the marginal cost, in dollars per square foot, of…

A:

Q: (3) If {f} converges uniformly converges uniformly on [a, b]. on (a, b) and {fn(a)} and {fn(b)}…

A:

Q: Determine whether the series is convergent or divergent by expressings as a telescoping sum. If it…

A:

Q: Which of the following are linear combinations of 0 1 -1 02 [ -42 -2] [23¹] [8²] 14 94 ° [224] -6-8…

A:

Q: Find the Laplace transform of the following functions. 8. f(t)= et√1+ sin2t

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: An initial investment of $35000 grew into an amount of $50000, when compounded continuously at an…

A:

Q: f(x) = 3 tan x. (a) Solve f(x) = -3. (b) For what values of x is f(x) < -3 on the interval π π…

A: (a) Let, f(x)=3tan(x) Now, f(x)=-3⇒3tanx=-3⇒tanx=-1⇒tanx=-tanπ4⇒tanx=tannπ-π4⇒x=nπ-π4where…

Q: Which answer is it?

A:

Q: Solve using undetermined coefficients. Use A, B, C and etc. for constants. (D^2+25)y=x^2 cosx

A: Given: D2+25y=x2cosx We have to solve the given differential equation using the method of…

Q: If w In(4) cos(2yz - 3), x = log(t), y = 4et² and z = sin(t3-1). Find d

A:

Q: Let S₂ be the portion of the paraboloid z = 9-4x² - 4y² on the first octant above the plane z = 1.…

A:

Q: Question 1 Let W be the set of all vectors of the form a) [α] b where -2a +6b-6c = 0 Lc -3 Determine…

A:

Q: Given the following system of equations Mt = g: a) Write Mt as linear combination of columns of…

A:

Q: Evaluate the geometric series or state that it diverges. 80 Σ e-22n n=0 Select the correct choice…

A:

Q: WORK PROBLEMS (6 Question 1 a) i b) c) s): You must provide a clear and detailed solution for each…

A:

Q: Question 1 Given the differential equation 3y" − 21y' + 36y = 3e-4² a) Classify the given…

A:

Q: Let f(x) = 5x³ (f¹) (2)= 2x LORE 1. Find (ƒ¯¹) '(2).

A:

Q: Not the right answer

A:

Q: Show sequence (-1)^n has uncountably many subsequences

A: The given sequence -1n. We have to prove that the sequence has uncountably many subsequences.

Q: Given the function f(x) = x²e8x, Determine the open interval(s) where the function is concave up…

A: Given: Function, f(x)=x2e8xTo find: a) Open interval for concave up              b) Open interval…

Q: 12. Find a) L-¹ [24+25 s²+25 + $²-9 10 b) - L -2)³

A:

Q: For each of the following series, determine whether the series converges or diverges. (Sum from 1 to…

A:

Q: 2X1 + 2X2 + X3 >= 1000   2X1 + 2X2 + X3 + X4 = 0   How is draw this graphic?

A: To draw the graphic for this system of linear inequalities, you can follow these steps.Here is a…

Q: If f(x) is a polynomial of degree less than 3, then prove that f(a) (x-a) 1 a +1 b f(b) (x-b) f(c)…

A:

Q: You open a brokerage account and purchases 100 shares of a stock at a price of $20 per share. You…

A: Given that, You open a brokerage account and purchase 100 shares of a stock at a price of $20 per…

Q: Find the eigenvalues and eigenvectors for the matrix A = 1 2 -1 0 -4 0 5 2 -5

A:

Q: Suppose that x = (2,1,0,3),y=(3,-1,5,2), and z=(-1,0,2,1). Which of the following vectors are in…

A: A vector v is said to be in the span of the vectors v1, v2, v3, ……, vn if the vector v can be…

Q: 50/² So So 11/2 1/4 ассс Ө фрарфрфин 2 p3 sin ²0 sin

A:

Q: 7. Find a fundamental matrix for the system *' (t) = A - *(t) for Го a. A = 0 L8 1 0 -14 01 1 7

A:

Q: Let T R³ →→→ R³ be a linear transformation such that T(1,0,0) (2, 4, -1), T(0, 1, 0) = (1, 3, —2)…

A: