3. z = x+y x-y

Q: dy Find the complete solution of 2e2¹ cosx- dx Note: [e"du=e" + C - sin² x = 0.

A:

Q: Find the particular solution of dy/dx=6e^3x+1,andf(0)=0.

A:

Q: a. Use the definition mtan = lim f(a+h)-f(a) h h→0 b. Determine an equation of the tangent line at…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: Find the area of the surface generated by revolving x=√(8y-y2) on the interval 2≤y≤5 about the…

A:

Q: 27. Which of the following function is continuous at x = 2? 2 2-3x A. f(x): = C. g(x)= = x-2 2-x…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the equations of tangent and normal lines of the curves at given points: y²-3xy - x = 0 at(2,8)

A:

Q: 14. For the series Σn=1 (-1)" 3n0.3+8 S4= Include 4 decimals in your answer. Now find a bound for…

A:

Q: Consider the vector-valued function R(t) = (t³-t, 2t², 2 - 21²). 1. Find ||'(t)||. (Simplify your…

A:

Q: _42. Evaluate: √(√√x - 2)dx 3 A. ++ C x 3 B. - + C x C. 3 +=+ C 2 D. -*²_³+C 2 x 12 Evaluato: ((2x…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

A:

Q: Determine the center-radius Form of the equation of the sphere who diameter has endpoints at (2, -3,…

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

Q: If fx √1- x4 dx = ge ½ A B 0 C D) 1 H|2 H|4 g(e) de, then 9

A: We can solve the given integral by using substitution.

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: topic - application of derivatives

Q: Consider the function. x³ + 12 f(x) = X Determine the intervals on which f is increasing,…

A: A function f (x) is increasing on the interval I if f'(x) >0 for x in I. A function f (x) is…

Q: . Expand the binomial (2x - 1)*.

A: Binomial theorem

Q: If z is a function of x and y implicitly defined by əz əz find and əx ду at (x, y, z) = (0, 2, -1).…

A:

Q: II. Consider the polar curves C₁ : r = 3 (in blue) and C₂:r = 2-2 sin (in red) and let R be the…

A: Given that polar curves  C1 : r = 3  and C2 : r=2-2sinθ  we have to find all points of intersection…

Q: dx ex√4-e²x the integrand is transformed into? (a) cos² 0 (c) sin² 0 (b) sec²0 (d) csc²0 When the…

A:

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. 1 S₁749 dx…

A:

Q: By method of Integration by Partial Fractions, A B(2x-2) + C (x³+5x²+6)dx (x²–2x+5)² = √ [₁²-2² +…

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

Q: Find the Area of the Surface obtained by rotating the curve about the x-axis y = cosh x, 0≤x≤1

A:

Q: Evaluate J (2a² y +9y³)dA, D is the region bounded by y www 33522 a. 5 O b. 4811 5 OC. None of the…

A:

Q: Let The coefficient of x³ in the Maclaurin series for f(z) is: Answer: . You may explain your answer…

A: The given function is f(x)=9e2x-x A Maclaurin series is given by:-

Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

A:

Q: 47. Evaluate: x(x² + 3)5dx A. (x²+3)6 + C 12 B. (x²+3)6 + C C. ²/(x²+3)6 + C D. (x²+3)6 + C

A: According to the company rule we can answer the first question and rest can be reposted.

Q: Given x = y²+2y 8 - In(y + 1), find the arc length for 0 ≤ y ≤ 3

A: Given: x=y2+2y8-ln(y+1) The arc length is: L=∫ab1+dxdy2dy Now, dxdy=dy2+2y8-ln(y+1)dy…

Q: Use the properties of logarithms to expand the logarithm as much as possible. Rewrite the expression…

A:

Q: Determine the area of the region bounded by x = ³√/y-1 from y = 0 to y = 1.

A:

Q: 2x fe²x sinx dx

A: Using integration by part.

Q: ds Find the complete solution of = 8t³ √s. dt

A:

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If Ř(0) = (-1,4,-5),…

A:

Q: x2 (x+2)³ dx In Ix + 2) + 4x+6 (x+2)² +C In Ix + 21 4x+6 (x+2) +C

A:

Q: Solve ₂(x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

A:

Q: d dx sinh(Vx)=

A:

Q: Find the area bounded by y³ = x² and x-axis, from x = 0 to x = 8.

A:

Q: Find the area bounded by the parabolas (x-2)²-9py = 0 and y² = 9p(x-2).

A:

Q: -5x² +11x+2 x(x+1)² dx 2ln|x| +3 In|x +1| + + + C x+1 Option 1 2ln|x| +3 In|x +1| +++ C Option 3…

A:

Q: (b) f is concave down on (-∞, 1) and concave up on (1, ∞). (c) lim f(x) = -∞ and lim f(x) = ∞. x-1-…

A: As per the guidelines we can solve 3 parts only

Q: 2. z = ²+² У Х

A:

Q: Evaluate the y' and Simplify the answers Inverse trigo functions y = √x² - 4+2arc(csc)

A:

Q: Considering C is a curve which has the following parametric equations: 1 t³t+1, C = { x (t) = { 1³3…

A: Parametric equation

Q: Find a particular solution of as =10csc² 2t determined by s= 2 when t == . dt

A: dsdt=10csc2(2t)  s(π/4)=2 ds=10csc2(2t)  take integration both side

Q: -x+1 3+z Given the points R (1, -1, -3), the vector v = and the line d: = 1 + y = 3 2 1. Determine…

A: Both questions are solved.

Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

A:

Q: xpand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of…

A: We  have simplify above questions

Q: Find the distance from the point P(1, 2, −1) to the line passing through the points A(−2, −3, −5)…

A:

Q: Find the transition points. y = 4x7 - 56x6 (Use symbolic notation and fractions where needed. Give…

A: Given that y=4x7-56x6Solution :if we find critical point then f'=0 and f' does not…

Q: A B D 0 Consider the integral f sin ¹x dx. If we let u = sin ¹x and dv = dx, the integral can be…

A: We have to above question

Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

A: Given

Q: Question Suppose a population of fruit flies increases at a rate of g(t) = 4e0.11, in flies per day.…

A: Given Population of fruits flies increases at a rate of gt=4e0.1t,per dayinitial population =380…