1 sinh x cosh3 x √9-cosh² x dx

Q: Find all points where the function has any relative extrema. Identify any saddle points. f(x,y) =…

A: f(x, y) =4x2+6xy+3y2-4x-8 In this question, we need to find all the points where the function has…

Q: Test for exactness, then solve.  ey dx + (2y + xey) dy = 0

A: This question is related to differential equations, we will solve it using given information.

Q: Find the area bounded by y = 2 - x² and y = x a. 9/2 b. 7/2 c. 5/2 d. 3/2 e. NONE OF THE ABOVE A D E

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Q: ૩ 3* sech³ (3) 1+tanh (3) S- -dx

A: Substitution method in integration: To simplify the integral, in the given integral independent…

Q: cos³ 3x sin 3x dx

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Q: The following differential equation is a Bernoulli equation: 2 dy + 27/ y3 where y = f(t) dt By…

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Q: Kindly write this, I cant understand by text

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Q: 3. S. 3*sech³ (3³) 1+tanh (3*) -dx

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Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

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Q: The choice of u and du is subject to trial and error. Identify the appropriate choice of u and dv f…

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Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: x² + x 1. lim x++∞ e²x + Inx 2. lim (sech 2x) esch x² +0+x

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Q: 1-coth² (log₂x) dx x cosh(log₂x) 1. 11/20

A: We have to find the integral.

Q: FIND X: 6.95460 = -0.658 + 1.41853 + 9.36 (log10 (X + 1)) + 0.40+ -0.20091 1094 (X+1)5.19

A: Given:  6.95460=-0.658+1.41853+9.36log10x+1 + -0.200910.40+1094x+15.196.19407=9.36log10x+1 +…

Q: Evaluate the limit using the L'Hopital's Rule. 1 - cosh x lim x→0+ ln(x² + 1)

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Q: Evaluate the multiple integral. * 131-x² SS S dz dy dx 100 0 2/3 5/3 4/3

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Q: -.f x³ ex² dx 3

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Q: So x² (a²-x²) ³¹/2² dx

A: A detailed solution is given below.

Q: Find the volume of the sould generated by revolving the area bounded by the _given curves about the…

A: Let's find volume of solid (V) = ?

Q: A ship leaves port travelling North West at 12 knots. A second ship leaves the same port 3 hours…

A: Given: Let first ship be Ship A and second ship be Ship B. Speed of ship A = 12 knots =12 nautical…

Q: The choice of u and du is subject to trial and error. Identify the appropriate choice of u and du…

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Q: answer a and b a. The marginal cost of manufacturing x tarpaulins is given by 0.03x2 + 0.4x + 7. If…

A: Explanation of the answer is as follows

Q: (Requires a short but nontrivial geometric argument.). Let ABC be a triangle with angles…

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Q: If F(x) a. F'(1) L √4t - t² dt, evaluate the following: x² b. F(2), by interpreting F(2) as an area

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Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

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Q: Determine the values of r for which the differential equation y" +9y' + 20y = 0 has solutions of the…

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Q: A solid consists of a right-circular cylinder and a hemisphere on each end. The length of the…

A: The diagram of the cylinder with hemisphere on the end will be as following To find dVdr at r=2,…

Q: Evaluate f(x³ -x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

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Q: 64 Lood (vt. 1 √t + √i) dt

A: Given ∫164(t-1t+t3) dtTo evaluate the Integral:

Q: Evaluate the following integrals S- 3 • │e* − e| + (e* + = e) + e) dx e 0

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Q: 4. Evaluate the double integral: L Lady. dx dy. 1/3 27 +1 (Hint: Change the order of integration to…

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Q: Find the absolute extremum points of f(x) = sin2 x + cos x on the interval [0, π].

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Q: 1.) +y=e+ dx=3e-t 2. .) d- given: x(0) = 0, y(0) = 1 dy-x=0 d+y=1 given a z (0) = -1, y(0) = 1.

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Q: Prove that d/dx(cos x) = −sin⁡ x using the definition of the derivative.

A: Given: fx=cosx   As we know from the definition of the derivative; The expression for the derivative…

Q: TU Evaluate sec²20d0 a. 00.33 b. 0.5 c. 0.67 d. 0.25 e. NONE OF THE ABOVE

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Q: 2 = 2(0)+7(0) + ²₂ D 6. Use a(t)=-32 feet per second squared as the acceleration due to gravity. A…

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Q: Find the area bounded by y = 2 - x² and y=x a. 9/2 b. 7/2 C. 5/2 d. 3/2 e. NONE OF THE ABOVE

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: The equation of the curves are: C1: y = x2 ⇒ x = y                 for first quadrantC2: x = y2 To…

Q: Q1-A/Find the domain of the following functions. 1-f(x) = √(sin(x) - 1) 2-f(x)=-/In(5x-x²/4)

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Q: Q3. Evaluate : IL (2) * dy dx

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Q: What is the y-coordinate of the centroid of the plane region bounded b y = x^2 - 4 and y = 2x - x^2…

A: Y coordinates of centroid of plane is given.

Q: 2. lim (x - Inx)* x)² 2-0+

A: Here, the given limit is: limx→0+(x-ln x)x which is (-∞)0 form.

Q: Draw a direction field for the differential equation y'= (y - 9)². Based on the direction field,…

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Q: 6. Find the area bounded by y= In x, y = 0 and x = e.

A: Area of a curve y=f(x) bounded by x=a, x=b is given by, A=∫abf(x)dx ln(e)=1, ln(1)=0

Q: 9. A child is flying a kite with a 45-ft string at an angle of elevation of 50°. Which of the…

A: Let's find altitude of the kite in feet.

Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: We have to find the marginal profit.

Q: 6. S t √1+2t dt

A: The given integral,    ∫t1+2t4dt

Q: Find the Integrating Factor (I.F) of the following linear differential equation: (1 + ²) + y = t…

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Q: Use the linear approximation to estimate In (√0.99).

A: Given problem:- Use the linear approximation to estimate In(3√0.99).

Q: An investment produces a perpetual stream of income with a flow rate of R(t) = 1,500 e 0.02t. Find…

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