To integrate 3x² e4² ΟΧ dx' we apply integration by parts and in the form u dv, u is set as:

Q: (x-7) dx 19. SJ5-4x-x2

A: Answer is following.

Q: where a represents the number (in thousands) of ten-packs demanded each week when the unit price is…

A:

Q: Find the gradient field of the function g(x,y,z) = 8xy + 2yz + xz. Vg= (Type your answer in terms of…

A: We have to find the gradient field.

Q: Find the derivative of sin In x O sin(Inx)/x O cos(Inx)/x O cos(1/x) O sin (1/x)

A:

Q: B. Find the general solution of the following 2nd order differential equation: y +2y + 2y = 0

A:

Q: Question 19 Given f(x,y) = ex cos y, Evaluate fx(0,2) A) e² B 0 (C) -sin 2 D) cos 2

A: Topic = Derivative

Q: 15 which of the following rule defines y as a function of X? Y = √x 16 which of the following rule…

A: Let's solve.

Q: 15 Ső 0 X √x+1 ах

A: We have to solve the given definite integral

Q: Solve the given ODE using the method of undetermined coefficients. y" – 4y = (x² − 3)(sin2x)

A:

Q: D. Diego walks at the rate of 5 ft per second toward a street light whose lamp is 20 ft above the…

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Q: If g'(6) = 6 and h'(6) = 19, find f'(6) for f(x) = f'(6)= (Simplify your answer.) () = g(x) + =…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

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Q: Which of the following is not true? A None of the given choices .3 dx dx S₁ in (x²) B lim S c+1+³c…

A: Let's solve.

Q: Solve what is asked in the following problems. Write your solutions and box your final answers 1.…

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Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

A:

Q: Test Content Question 9 In evaluating Add your answer 5 dx is same as evaluating lim (In(f(x))).…

A: The integration of the integral is 1/sqrt(x2-9).

Q: Evaluate the following definite integral using substitution rule. 1. (2x - 1)² dx 2. fx √x² + 1 dx

A:

Q: Find the slope of the tangent line to r²e³ + y²e² = 2e at (1,1).

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Q: a. The object's velocity after 5 seconds is (Round to the nearest tenth as needed.) m/sec.

A: We have to find the velocity after 5 sec

Q: x6 cos(x³) |dx=0

A: Follow the procedure given below.

Q: 7. fcsc (3x) • cot (3x) dx csc(3x) A. + C B. -csc(3x) 3 + C C. -3 csc(3x) + C

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: In evaluating x=3.98. dx x²-9 is same as evaluating lim (In(f(x))). Determine the value of f(x) if…

A: First we evaluate f(x) using substitution

Q: 1. Jổ xdx xdx ull ch 2. √²2² (x²-x)dx 3. f2, xdx

A: We have to solve as per guidelines Solving by fundamental theorem of calculus

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: Given problem:- Find the volume of the solid generated by revolving the area bounded by the given…

Q: For the given function f(x,y)=x²y³+3x³y, find a flay O 2xy3+9x² y O 3x²y²+3x³ O 6xy²+9x² O 2+18xy

A: We have to define the derivative

Q: dx 8. √√√√x+√√x

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Q: - 2500q, what cost is incurred when marginal profit is $0? Given Cost and Revenue functions C(q)…

A: In this question, we need to find the cost when the marginal profit is $0.

Q: Let F(x) = f(x¹) and G(x) = (f(x))¹. You also know that a = Then F'(a) = = 12, f(a) = 3, f'(a) = 4,…

A: Fx=fx4 and Gx=fx4a3=12, f(a)=3, f'(a)=4, f'a4=7

Q: Which of the following is commutative with respect to addition? 8x3−y6=… Complete the following…

A: Which of the following is commutative with respect to addition? 8x3−y6=… Complete the following…

Q: ex = cosy

A:

Q: 2. Let S be the part of the cone z = √² + y² that lies between z = 1 and z = 3 with upward pointing…

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Q: dx 20.5 x√4x²-49

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Q: 4. fx√x - 3 dx

A:

Q: 3n³ + 2n² + 1 n→∞ 1+n-2n³ " (a) lim (b) lim x→1 x² + √√√x-2 1 - ln x

A: Topic = Limits

Q: If f is continuous on A) True B False on [a,b], then Sº [ f(x a xf(x) dx = x f(x) dx

A: It will solve by part method integration  ∫u v dx = u∫v dx −∫u' (∫v dx) dx u is the function u(x) v…

Q: blanks 1 3. The angle between vectors A = 91-j+5k and B=(-2,7,1) is...... 4. If = (-12,4,8) the…

A: ssolution given below

Q: Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 3), and (2, 0).…

A: SOLUTION-

Q: Q2. Find the exponential Fourier series for f(t): (1 = Fourier series. 0<t<1 (2 1<t<2 then find the…

A:

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

A:

Q: A ladder 20 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: d the area of the surface obtained by rotating the line y = 19x + 6 about the x-axis from point…

A: Topic:- application of integration

Q: For the function y =f(x), it was found out that f(c) = 0. What can be said that x=c? O critical…

A:

Q: da potential function f for the field F. F = (4y + 2z)i + (4x+z)j + (2x+y)k eneral expression for…

A: Topic:- application of integration

Q: Find the determinant of the matrix. O-31 -4 67 7

A: det-46127Use deta  b c  d  = ad-bc=-4· 7-6·12=-31

Q: Fill in the blanks the information needed to make the solutions correct.

A: 1)∫23(t3+5) dt2)∫12(x2-x) dx

Q: Solve for x. O-1,-4 O -1,4 O 1,4 O 1,-4 x-1 3 2 x-2 =0

A: Given,      x-132x-2=0

Q: Find the length of the arc of a circle of diameter 1010 meters subtended by a central angle of π4π4…

A: Solution ) diameter - 1010 m , angle = π/4 Radius =  1010/2           = 505 m length of arc of…

Q: 6. f cos¹ 2 xdx

A: Given,  ∫ cos7 2xdx

Q: Consider the function f(x) exact values. f'(x) = f''(x) = f'''(x) = = Compute each of the following.…

A: Topic:- derivatives

Q: To integrate x3 exdx, we apply integration by parts and in the form u dv, dv is set as: O ex dx O…

A: We have to find the dv