a) Find the linear approximation of f(x) = Vx b) Use it to approximate V26.9 at x= 27 %3D

Q: Evaluate the limit sin 3x lim 9x

A:

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

A:

Q: Find T(t) and N(t) at the given point. r(t) = (t – 2)i + tj; t= 2 T(2) = N(2) =

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x3…

A:

Q: Conjecture a formula for f'(a) that depends only on the value a. That is, in the same way that we…

A: Given that, fx=4x-x2 We need to compute the value of f'a.

Q: 1. Identify the type of conic section whose equation is given, then find the vertices and foci.…

A:

Q: If the angle between the vectors A = xâ, +â̟and B = /3â, +â, is 60°, find x.

A:

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: dy Find dx 4t t dt + 2 y = dt - t° + 2 - 3 6. dy dx (Simplify your answer.)

A:

Q: Show that (1-)" =e= %3D Which of the series converge and which diverge. 4n+3 (1) E=14 m%3D1 (-4)"…

A:

Q: Find the position function s(t) given acceleration a(t) = 2t if v(2) = 0 and s(2)=1.

A:

Q: 3. a) If 2 - i is a root of x³ – 2x² – 3x + 10 = 0, find the other complex root. b) Calculate the…

A:

Q: 12. L(s? – 1) sds 13. (1² – #) dt

A: ∫xndx=xn+1n+1+C , C is a constant for any real number n.

Q: S cos³ 3x dx со

A:

Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 4 1 lim t→+∞ \ 8t2 +9' 4t |(?, ?)

A:

Q: Find the value of (5a² – 6)da

A: This is a problem of integration. Based on the formula and concept we will answer the question.

Q: 75 then compute the limit. 137 2| %3D Investigate the one sided limits (left and right) of f () =…

A: Given query is to find the limit.

Q: Find the average value fave of the function f on the given interval. f(x) = 18x – x², [0, 4] fave…

A:

Q: Given that 5i is a zero of p, write the polynomial in factored form as a product of linear factors:…

A: Given that the polynomial is a6-11a5+65a4-331a3+1024a2-1400a+600 and 5i is a zero of the polynomial.…

Q: Estimate cos(π/4 - 0.1) + cosπ/4

A: Solving

Q: Determine whether the integral is improper (x-4) -'dx A Improper B Not improper

A: Given data÷

Q: Activity 1.4.3. For each of the listed functions, determine a formula for the derivative function.…

A:

Q: The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.02t° +…

A: This question can be solved using the concept of interpretation of a function and its derivative at…

Q: certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 59 - 2.2t…

A: Given query is to find the average temperature for the given time interval.

Q: A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches the…

A: Let x be the acute angle made by the telescope with the vertical.

Q: 4. sec 4x tan 4x dx

A:

Q: is xZ dz dx dy

A:

Q: Obtain the general solution for the following differential equation. (a) y" – (a + ß)y' + aßy = 0 (a…

A: To solve the higher order differential equation.

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

A:

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 average value gave of the function g on the given interval. g(x) = 3x, [8, 64] gave =…

A:

Q: Find the tangent equation for the function: f(x) = Vx2 +5 at x=2? Find the limits by using L.Hopital…

A:

Q: Determine the value of 5A+6M if 2x4 + 3x3 +8x2 + 14x + 3 A x-3 х — 3x + M - x(1 + x2)2 1 +x2 (1…

A:

Q: 5. If x = 5cis(2.945)and y = cis( – 0.755) find xy³. Leave your answer in polar form. Note the…

A: If x=5 cis2.945 and y=cis-0.755, then to find xy3.

Q: The world population was approximately 6.04 billion at the beginning of 2000. It has been estimated…

A:

Q: Find a power series representation for the function. Determine the interval of convergence. (Give…

A: Given f(x)=58-xwe know that the power series11-r=∑n=0∞ rn

Q: Given that u= and v= and that u.v= 199 determine the value of the constant A. Answer:

A:

Q: The discontinuities of the function f(x) = %3D 4х-9 are: х2—2х-15 Select one: O 5,3 O -5, -3 -5,3 O…

A:

Q: Let u= and v=. If uX v= then determine the value of 3A+B+C. Answer:

A:

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A: Given that the population of mosquitoes in a certain increases at a rate proportional to the current…

Q: Let C1 be the curve with parametric equations x = cost, y = sint – t, where t e [0, 5]. (a) Find the…

A:

Q: 1 Find Vf if f = 2 /x²+y² +z?

A:

Q: 1. Consider the curve defined by 9x2 – 16 y² + 36x + 96 y– 252 = 0. a) Write the equation of the…

A: To solve the following problem

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: e velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2 -…

A:

Q: Find the arc length L of the graph of r(t). r(t)= 4 cos(t)i + 4 sin(t)j + tk, 0 ≤ t ≤ 2π

A: The formula for the arc length is given by: L=∫02π(x'(t))2+(y'(t))2dt Here,…

Q: Find the interest and amount due on a loan of Php 54,000 at 15.6% per year for 100 days.

A: Find the interest and amount due on a loan of Php 54,000 at 15.6% per year for 100 days.

Q: is said to be the Laplace transform of f, provided that the integral converges. to find L{f(t)}.…

A: Let's find.

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the…

A:

Q: 7. The ellipse with the equation y2 = 1 is rotated about the x axis to form a solid shape. A…

A: Given:  An ellipse:x252+y242=1  , rotated around x-axis. A cylinderical hole of radius 2cm along…