dy Assume x and y are functions of t. Evaluate for the following. dt dy dt 3 y³ = 2x³ + 10; || dx dt = 2, x= 3, y = 4 (Round to two decimal places as needed.)

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: ∫6∞ xe-x3dx

Q: 2. Prove div(curl(F) = 0, if F = Pi + Qj+ Rk is a vector field on R³ and P, Q and R have continuous…

A: Let us prove that div. curl F=0 Given:F=Pi+Qj+Rk is a vector field  in ℝ3To show that:∇.curl F=0

Q: Find + 12 10 .12 [9f(x) = g(x)]dx if [9f(x) = g(x)]dx = i 12 [2² 10 f(x)dx = 9 and 12 10 g(x)dx = 8.

A: integration

Q: Find the mass of the lamina that occupies the region D = {(x, y): 0 ≤ x ≤ 1,0 ≤ y ≤ 1} with the…

A:

Q: The graph of f' (not f) is given in the figure. At which of the marked values of x are the following…

A:

Q: In(x) x² -dx

A:

Q: Please help to solve this into detail. Thank you.   1) Find an equation of the plane tangent to…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: t After a patient takes a medication the amount of drug in the bloodstream (in my per L) after +…

A: A=20e-0.35td dt(et)=et

Q: Find the points on the surface y² = 81 + xz that are closest to the origin. smaller y-value (x, y,…

A:

Q: Find the absolute maximum and absolute minimum values of f(x) = x³ + 3x² − 45x-10 on [-8, 2] along…

A:

Q: Evaluate the definite integral by expressing it in terms of u and evaluating the resulting integral…

A:

Q: 2 1) Fird dy using implicit differentiation X² + y ²³ = 7xy 2) Find the ein of the normal line to…

A:

Q: Find f-1 (x) for f(x) = - 5 3x-2 O f-¹(x) = ³xx 3x-2 5x O f-1(x) = -3x + 2x 5 3x 2 O f-¹(x)= ³x-² 5…

A: In this question, we want to find the inverse of the given function.

Q: Meteorologists define the temperature lapse rate to be -dT/dz where T is the air temperature in…

A:

Q: 9. Determine the equation in the form 1 f(x) = kx for the function with a vertical C asymptote at x…

A: To determine the equation in the form fx=1kx-c  for the function with a vertical asymptote at x=-1…

Q: Find the component forms of v+w and v- w in 2-space, given that ㅠ ||v|| = 7, ||w|| = 3, v makes an…

A:

Q: Find a second-degree polynomial P such that P(1) = 1, P'(1) = 4, and P"(1) = 8. P(x) = = Need Help?…

A: letP(x)=ax2+bx+cgiven  P(1)=1P'(1)=4p''(1)=8we know  d dx(xn)=nxn-1

Q: QUESTION 1 If f(x)=x and g(x)=k-x are orthogonal over [0,1]. Then k = ..... O 1 O O N/W W/A W/ W/N…

A:

Q: Triangle ABC has vertices A(4, 7, 7), B(1, 6, 5), and C(–2, 9, 8). Which kind of triangle is ΔABC?…

A:

Q: Given t(x) = 2x² - x. a. Find the point of tangency to the curve at x = 3 b. Use the definition of…

A:

Q: 10. S 1 x²+2x dx

A:

Q: 2) Find the derivative of the function f(x) = *³-2x x²

A:

Q: |B| = = B²} + B² + B²

A: The expression |B|=√(B^2x+ B^2y+ B^2z) represents the magnitude or length of a three-dimensional…

Q: a. Find the Laplace transform F(s) = L{f(t)} of the function f(t) = 2 + sin(6t), defined on the…

A:

Q: Use the following function and its graph to answer (a) through (d) below. Let f(x) = choice. 6-x,…

A: Given function:- fx=6-xx<4x+1x>4 Graph of function

Q: Let u = (5,5), v = (1, 3), w = (17,-4). Find the vector x that satisfies 3u2v + x = 6x + w. NOTE:…

A:

Q: Find the norm of v. NOTE: Enter the exact answers. (a) v = (6, -6) ||v|| = (b) v = -6i+2j ||v|| = =…

A: We have given vectors  a v=<6,-6> v=62+-62=36+36=72 v=62 b v=-6i+2j v=-62+22=36+4=40 v=210 c…

Q: U.S. Cell Phone Subscribers The number of cell phone subscribers in the United States between the…

A: Given: N(t) = 385.4741+2.521e-0.214t for (0 ≤ t ≤ 10) , where N(t) is measured in millions and t is…

Q: The mass of the disk is given by m = f 2xр (x) dx, where p(x) is an integrable function representing…

A:

Q: The region in the first quadrant between the x-axis and y = x² from x = 0 to x = 4 is rotated about…

A: The answer is in step 2.

Q: Textbook Videos [+] If f(x) = 3r(sin x + cos z), find f'(x) = f'(2) = Question Help: Video Message…

A: f(x)=3x(sinx+cosx)d dx(sinx)=cosxd dx(cosx)=-sinx d dx(xn)=nxn-1

Q: x+y2 - x5y + 4xy3 = 0 X

A: Given query is to find indicated derivative.

Q: Evaluate sinh -1(4/3)

A: Given: sinh-1(4/3)

Q: Answer: Compute the value of the following improper integral. If it is divergent, type "Diverges" or…

A:

Q: Write a mathematical model for each of the following statements. Use k as the constant of variation.…

A:

Q: Absorption of Drugs The concentration of a drug in an organ at any time t (in seconds) is given by…

A: x(t)=0.09+0.16(1-e-0.013t)(i) for initial condition put t=0

Q: Solve the following differential equations. sin x)dx 1. dy=[ytan x + +e²x

A: We can solve it as below.

Q: The profit (in dollars) from the sale of x lawn mowers is P(x) = 30x -0.03x² - 750. (A) Find the…

A:

Q: Use closed interval method to find the absolute max and min values of f(x)= x/(x^2 +2) on the…

A:

Q: Find the area of the region bounded by the graphs of the functions: f (x) = sin 2x and g(x) = cos 4x…

A:

Q: 18. fcot'0 sin¹0 de 20. f cos³x sin 2x dx 22. ² sec (1/2) di

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Differentiate the function using one or more of the differentiation rules. y: 1 = (3 + 2x5) 5 y' =

A: We know that, The SUM/Difference Rule: f±g'=f'±g' The Power Rule: ddxxn=nxn-1 The Chain Rule:…

Q: Find and sketch the level curves f(x,y) = c on the same set of coordinate axes for the given values…

A:

Q: Find the limit by rewriting the fraction first. xy-y-3x +3 X-1 lim (x,y) →(1,5) x #1 lim (x,y)…

A:

Q: A search using the web search engine BingTM for "asteroid" yielded 25.1 million web sites containing…

A:

Q: Consider the following. u = (5,5), v = (4, 6) (a) Find the projection of u onto v. (b) Find the…

A:

Q: Using the Inverse Function Theorem, what is (s−1)′(1) given that s(x)=3x3+6x2+9x+7? Note that…

A:

Q: ƒ'(x) = (x+4) (12 — x)(x − 16)

A:

Q: Write a mathematical model for the following statement. Use k as the constant of variation. s varies…

A: We have given a statement  s varies directly as square of t sαt2 s=kt2

Q: Find the volume under the graph of the function f(x, y) = 10x²y over the region shown in the figure…

A: Consider the region