2) a) Find the unit vectors that are parallel to the tangent line to the curve y = 2sinx at the point b) Find the unit vectors that are perpendicular to the tangent line

Q: Evaluate the double integral: L y 1/3 27 +1 dx dy.

A: Given: I=∫08∫y132yx7+1dxdy The region bounded by the curves x=y13, x=2, y=0 & y=8 is as shown…

Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(8y) dy =…

A: Let's solve given diffrential equation.

Q: 1 If sin(0) and is in the 4th quadrant, find cos(0) 8 cos(0) = Enter your answer as a reduced…

A:

Q: QUESTION 2 Given: 2y (y2-x) dy = dx ; x(0)=1 Find x when y=2. Use 2 decimal places.

A:

Q: Evaluate the double integral over the rectangular region R. x√9 - x²dA R = Mi [[ x√√9 – x²dA; R =…

A:

Q: The region D bounded by y=0, x=y - 1, X x = as given in the following figure. YA 3.0+ 2.5- 2.0+ 1.5+…

A:

Q: F Find the area of the region bounded by the curve y = x³ and the lines y = -x, y = 1. (Draw the…

A:

Q: The function f(x) = 2x³ - 30x² + 144x + 6 has one local minimum and one local maximum. Use a graph…

A: The given problem is solved below in detail.

Q: luate 2 Af ² (x-1) 25 dx 7 S² √4+3x dx 1 x² (1+22³)5 dx esinx cosxdx O 플 the definite O inte

A:

Q: An airplane takes 3 hours to travel a distance of 1560 miles with the wind. The return trip takes 4…

A: This question can be solved using the concept of speed,time and distance.

Q: Problem 4. (. Let C be the curve given by parametric equations y(t) = 2t, z(t) = lnt, t€ (-∞0, +∞0).…

A:

Q: For a particular financial methodology, the risk-reward function was defined as y=x(Inx-2), where y…

A:

Q: R, S and T are closed sets implies RnSnT is closed.

A: given

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 3x)y², y(0) = = 2…

A:

Q: Find a differential equation that corresponds to the given direction field. Consider differential…

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) COS(π/X9) dx x10 Need…

A:

Q: Consider the function f(x) = x¹ − 50x² +11, x¹50x² This function has an absolute minimum value equal…

A: We need to find absolute max. and min. value.

Q: Integral Evaluate the √x (x-²) ³ dx

A:

Q: Find the antiderivative of f(x) = point (0,3). O F(x) = tan¹x +1 O F(x) = 2 tan ¹x +1 -1 O F(x) =…

A: Given: fx=24x2+1 and x,Fx=0,3   As we know the expression for the antiderivative; Fx=∫fxdx And…

Q: Solve the given differential equation. All solutions should be found. (3y² + 2xy) dx − (2xy + x²) dy…

A: A detailed solution is given below.

Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x+4) in the interval…

A: Given: y=2x-123x+4

Q: 10. 11. 12. [V² da [v¹ de [5 V/210 de

A: We need to evaluate integral. As per Bartleby's guidelines we can solve only 3 subparts. Please…

Q: Evaluate y' y = cosh²12x +sinh²6x

A:

Q: Let A be the curve containing of the line segment from (0, 0) to (2, 0), the portion of the circle…

A: Given: A is the curve containing the line segment from 0,0 to 2,0 to the portion of the circle…

Q: Find the volume of a right pyramid that has a square base in the xy-plane. -1 ≤ x ≤ 1, −1≤ y ≤ 1,…

A: We have to find the volume of pyramid.

Q: Evalu‎ate ∫C (x + 2y) ds, w‎here C is the cu‎rve defi‎ned by y = √(4 − x2), for x ∈ [0, 1]

A:

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

A: We know that, Newton’s law of cooling is given by, dT/dt = k(Tt – Ts) Where, Tt = temperature of…

Q: he function f(x) - 2x³ 30x²+144x + 6 has one cal minimum and one local maximum. Use a graph of the…

A: Please refer to the image below

Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

A:

Q: Use the Fundamental Theorem of Calculus, Part 1 to find the derivative: d •√x (t² + Int)dt dx Sa

A: First I have written the Fundamental theorem of Calculus and using it for given problem and find the…

Q: Determine the combined moment about O due to the weight of the mailbox and the cross member AB. The…

A:

Q: EXAMPLE: (0,0) 3x-2y 26 5x+45 O > 5 x a 1915 CRITICAL POINTS -A (30) ( B (2.0) 1 D ( ¾/5,9). ✓c…

A:

Q: Find the area of the surface generated by revolving about x-axis the part of the curve y = sin x,…

A:

Q: solution

A: Please refer to the image below

Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², z(t) = lnt, t€ (-∞0, +∞0).…

A:

Q: (1² +21) dx dt = = 2x + 2 (t, x > 0), x(1) = 1

A: Given that: (t2 +2t) dx/dt  = 2x+2 ; x(1)=1. Find the solution of this initial value problem.   Here…

Q: Water is flowing into a conical cistern at the rate if 8 cubic m/min. If the height of the inverted…

A:

Q: 9 of 11 Approximate the area using a. Left Riemann Sum b. Right Riemann Sum c. Midpoint Riemann Sum…

A: Find out  the area using following Riemann sums.

Q: For the curve xy + x2y - xy² = 1, use implicit differentiation to find the equations of the tangent…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: Test for convergence/divergence, State the theorems used.

A: As per guidelines, I can answer only one question. Since questions are not interlink with each…

Q: dt 1³ +1²-2t

A:

Q: Find the characteristic equation, the eigenvalues,

A:

Q: Use Cartesian coordinates to evaluate y² dV D where D is the tetrahedron in the first octant bounded…

A:

Q: hand written plz 1 5. Let D be the region bounded by the lines y = x, x=3 and the curve y = (a)…

A:

Q: (2xy-sinx) dx + (x² - cosy) dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution of the…

Q: Use Taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when 0.5 ≤ x ≤…

A: We have to use Taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when…

Q: Apply Green's Theorem to evaluate the integral. $(3y + x)dx + (y + 5x)dy C: The circle (x - 3)² +…

A:

Q: 5TT Without using a calculator, compute the sine and cosine of 6 What is the reference angle? In…

A:

Q: 1. Given the region bounded by the following functions as well as the x-axis: y= 2²/1₂ ² x= x = 4…

A:

Q: O By direct partial integration, Solve the following PDES 8- аги axdy = CBX COSy? SXUCX,t) Ex u(x₂)…

A: The pde is solved using partial integration