An oil tank is being drained for cleaning. After t minutes there are Vlitres of oil left in the tank, where v) = 10(10 - )², 0

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

A: Using substitution ,

Q: 8- Prove that lim,. -7 (5x – 32) = 3 using the formal definition of the limit. (choose e and 6 )

A:

Q: 3. Find the general solution of the differential equation. y"-6y' +13y = 0.

A:

Q: z = 0, y = 1, у %3D1, z = x² + y? y = x².

A:

Q: Ley y = tan x. (a) Find the differential dy. dy = (b) Evaluate dy and Ay if x = t/3 and dx = -0.1.…

A: (a) Here f(x)=y=tanxdy=f'(x)dxdy=sec2xdx    =sec2(π3)(-0.1)    =-0.4

Q: Describe the graph of the equation. r = -6i+ (1 – t?)j + t k O It is a parabola in the plane z = -6,…

A:

Q: Determine the value of 3A+1OB if 14x2 + 33x + 9 Cx + B %3D (x – 1)(x+ 1)2 x - 1 (x + 1)2 Answer:

A:

Q: Find the arc length of the graph of r(t) = ev2ti+ e¯v2tj+ 2tk, 0<t < v2 In 5 NOTE: Enter the exact…

A:

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). ||r'(t)||³ r(t) : = 11 cos(3t)i +11 sin(3t)j +…

A:

Q: 5. S 2x' dx 6. S*-5x* dx x3

A:

Q: (6) At the start, an experiment records 1 gram of bacterial culture, and the culture's weight is…

A:

Q: 1+x+y dzdyax Jc JO Jo

A: To evaluate the given iterated integral.

Q: Find the value of the limit: lim x→0* sinx+ tan x

A: Given query is to find the value of the indicated limit

Q: Find S(sin20cose + cos30)d0

A:

Q: Let й —, i = where A and B are some constants. Given that ủ + 40 = find the value of the product…

A:

Q: How many terms of the series (-1)" 1+2" are needed to compute the sum of the series with an error…

A: By Alternating series estimation series test : s=∑n=1∞(-1)nbn        1)  bn+1≤bn2)  limn→∞ bn=0Then…

Q: y = 2 ||

A: We have to find the derivative of the function y = 1-x2ex2

Q: Evaluate: S(4sin (x) – 3sec? (x)) dx

A: ∫ 4sinx-3sec2xdx=∫ 4sinxdx-∫ 3sec2xdx=-4cosx-3tanxAdd a constant to the solution=-4cosx-3tanx+C

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) a + bxº dx 10ax + bx10

A: Evaluate the indefinite integral

Q: 6x7 – 5Vx + 3x + 4x-2 dx

A:

Q: dy Find dx of æ³ – y? = 5 by implicit - differentiation and evaluate the derivative at this point:…

A: According to our guidelines, we can answer only one question or three subparts of a question, other…

Q: nswer.

A:

Q: Consider the function. x - 8 f(x) x + 3 Step 1 of 2: Find all values of x that correspond to…

A: The given rational function is: f(x)=x-8x+3      =x+3-11x+3…

Q: Solve e2x + 7e*+6= 0 Show every step.

A: We have to find the value of x according to the given information

Q: Use the Laplace transform to solve the given initial-value problem. 2y" + 3y" — Зу' - 2у %3D е",…

A:

Q: d) Classify the differential equation as separable, exact, homogeneous, or Bernoulli. The equation…

A:

Q: -2 Evaluate (5y- 2)dy

A: Given problem :- Evaluate∫125y4-2dy

Q: APPLICATION I. Find the antiderivatives of the following functions using the substituion rule. Write…

A: Solving the problem by finding the value of the integrals.   NOTE :: As per our Expert guidelines we…

Q: Integrals

A:

Q: Obtain the value of P3 (x) using Rodrigues' formula d" P,(x) = (x² – 1)" (2")n! dx"

A:

Q: An airplane takes off from an airport at sea level and its altitude (in feet) at time t (in seconds)…

A: We have to find rate of climb of airplane at t=180 sec.

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

A:

Q: Write the 4 x 4 elementary matrix which accomplishes the row operation R3 - 5 R2 ---> R3 when you…

A: let  I be the 4×4  identity matrix I=1000010000100001

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

A: Given data÷

Q: Find the radius of convergence, R, of the series. (x + 4)" R Find the interval, I, of convergence of…

A: The given series,        ∑n=1∞n6nx+4n

Q: Find the arc length of the graph of r(t) = ev2ti+ e¯v2tj+ 2tk, 0<t< v2 In 5 NOTE: Enter the exact…

A: Let's find.

Q: d²y 2. Find the second derivative, dx² a. x = t² + 1 and y = t³ b. x = - t2 + 2 and y = sin(t+ 1)

A: Let's find.

Q: Differentiate the function. g(u) = 7u + V 5u

A:

Q: Evaluate the limit sin 9x lim I0 sin 3x

A:

Q: Convert the point from spherical coordinates to rectangular coordinates. (2플) (х, у, 2) -

A:

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

A:

Q: Given two points P1(0,2,-1) and P2(2,0,-1), find the perpendicular distance from the point P3(3, 3,…

A:

Q: Evaluate the Laplace transform of ecos3tdt. O a. s2+2 s2(s² + 4) Ob. s+ 16 Oc. 2 s(s²+ 16) O d. s?+4…

A:

Q: Find the general solution of the following nonlinear first order ariable separable O.D.E.: x?dy +…

A:

Q: Find the value of V®dx 0.

A:

Q: Q3) A) If you have three functions: f(x) = x2 – x g(x) = 3x – 1 %3D w(x) = x2 – 2 So, find gof (x)…

A:

Q: Solve the following problems. 1. A thermometer reading 18°F is brought into a room where the…

A:

Q: dy Q4) Find for the following functions dx 1. y = 2x? + e2x-1 2. y = sec x tan x 3. y = t2 + 2t t =…

A:

Q: 12. The Statue of Liberty is 150 feet tall and stands on a 150 foot pedestal. How far from the base…

A:

Q: B) Find for the Implicit function: dx x? – sin(xy) + y? = 5xy

A: The given equation is; x2-sin(xy)+y2=5xy.