lim,+-1 f(x) = $1 # 1 affe # HE 3 52 #1 0 EM 0

Q: Calculus optimisation problem Amount of fuel 'F' (in litres) required per hour to propell his…

A: Given, F(u) is the fuel in liters required per hour. u is the speed in kn/hr u(max)= 40 km/hr F(u)=…

Q: Please

A: Please refer to the image below

Q: Find f'(-2) if f(x) = 3 -7x. f'(-2)= (Simplify your answer. Type an integer or a fraction.)

A:

Q: 2. Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed,…

A: solution:-left end pointRiemann sumnumber of rectanglen=5∆t=10-05=2t0=0, t1=2,  t2=4,  t3=6,  t4=8,…

Q: Calculate the integral approximation S6 for 0 -1 4-² dx.

A: In this question we have to find the Integration.

Q: The function H(t) = −16t2 + 48t + 12 shows the height H(t), in feet, of a cannon ball after t…

A:

Q: A geometric series has S3=37/8 S6 = 3367/512 Find the first term and common ratio

A: Given, S3=37/8  S6 = 3367/512

Q: Find where the curves intersect, draw a sketch of the region (label it completely), and compute the…

A: This question can be solved using area bounded by curves.

Q: The median weight of a boy whose age is between 0 and 36 months can be approximated by the function…

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Q: Calculate M6 for f(x) = √7x on [0,2]

A:

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: 3) [₁ 10etan (e³x – 3) dx

A:

Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

A:

Q: Convert x = = ln(2t) and y = 1² from parametric to rectangular form. 2

A: Given,  x=ln(2t) and y=12t2

Q: 5. Lim xsinx x-0+

A: Let A=limx->0+xsin x

Q: Evaluate the following integrals by parts 5) f x1 x ln x dx

A:

Q: In problems 5 and 6 find the particular solutions of the given differential equations. d²y dy +9y =…

A: To find the solution of the given differential equation.

Q: Find the parallel projection of the vector v = onto the vector w=.

A: Given problem:- Find the parallel projection of the vector v=<4, -5, 7> onto the vector…

Q: Convert 2xy + 2 = 0 from rectangular to polar form and solve the resulting equation for r. r =

A: Given

Q: 3. Let u = f(x, y), x = r cos 0 and y = r sin 0. Show that: 1 1 Urr + −Ur + - U00 = Uxx + Uyy. p2 r

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Q: [f(a)]² =

A:

Q: Given cos(8)= - 5 m<8<³ 2 for π<8<- then tan(0) =

A: We can find the answer as below.

Q: In 23 In y SS 10 Evaluate the integral The value is. (Type an exact answer.) ₂x+y dx dy.

A: The given integral,     ∫0ln 23∫0ln yex+ydx dy

Q: Find the eigenvalues λ₁ < ^₂ < 3 and associated unit eigenvectors ₁, 2, 3 of the symmetric matrix 0…

A: Solve by matrix

Q: Question 13 Find the area of the region between the graphs of y=10-2² and y=-3z-30. The area is

A:

Q: What is the average rate of change of y with respect to over the interval [3, 5] for the function…

A: topic- average rate of change of function average rate of change for linear equation is equal to its…

Q: 18 1510 18 50 Change the Cartesian integral - Change the Cartesian integral into an equivalent polar…

A:

Q: π.χ. Evaluate the integral 8x sin y dy dx. 00 The value is. (Type an exact answer, using as needed.)

A: The given integral,    ∫0π∫0x8x siny dy dx

Q: 3. Find 1. Lim f(x) 2. Lim f(x) 3. Lim f(x) 4. Lim f(x) n→∞0 n→ ∞ n→0+ n→0- x < 0 When f(x) = -&…

A:

Q: Question 16 Find e > 0 such that the area of the region enclosed by the parabolas y = 2²-² and…

A: Given problem:- Find c&gt; 0 such that the area of the region enclosed by the parabolas y = c2 -x2…

Q: The vertical face of a dam has a height of 50 m and width of 600m. What is the total fluid force…

A:

Q: 2) Find AB and BA if : A = [1 2 3], 405 B = 0 -6 -7 8 9 10 -11 6] 7 -8.

A: For matrix multiplication , the number of columns in the first matrix must be equal to the number of…

Q: 35. √2x³ = 9x³ - 3x + 1 x³ = x² dx

A:

Q: Evaluate z² 3 y² sin z6 dx dy dz

A: Given: ∫01∫0z2∫03y2sinz6dxdydz

Q: 4. Find 3x 2t dx/e²t dt

A:

Q: Find the volume of the region bounded above by the paraboloid z = x² + 2y² and below by the square…

A:

Q: Write an equation for the transformed logarithm shown below 5 4 3 2 1 -5 -4 -3 -2 -1 3 4 5 f(x) = N…

A:

Q: Let f'(x)=(x-1)(x-3). Then f is increasing on a) (-∞,1]U[3,0) b) (-0,2] c) [1,3] d) [2,00)

A: Let f'x=x-1x-3

Q: Using Root Test the series Σtan where n 7n4 an = 3n4 + 4n - 5 diverges since 7 lim an == n→+∞ 3 the…

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Q: Find all critical points of f(x) = 4x³ + 4x-3. (Use symbolic notation and fractions where needed.…

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Q: An architect is asked to design a game room in the shape of an isosceles trapezoid where the non…

A: Let's find fourth side length for maximum area.

Q: 1.Find dy/dx of the following: 5. y = Incose* tan x 6. y = ln(1-xe) 7. y=eta et 4. y= In x 8.…

A:

Q: Consider - 9 dx. Using rationalizing substitution, we let z = √√e*-9. √√e²-96 What will be the form…

A: The integration of the integral is √(ex-9).

Q: What is the vector that results from transforming a by the transformation matrix? 5 ā= [ and B= -3…

A: The transformed vector can be obtained by multiplying matrix B with a→.

Q: (D² - 6D+9)y = 0

A:

Q: Compute the missing terms in the arithmetic sequence. 72, **** 1)..., 24,

A:

Q: Suppose F(5) = -4, F(6) = 4, and F'(x) = f(x). Sº f(x) f(x) dx = = Quest

A: Given problem:-

Q: dy Use Picard's method to solve =-xy, y (0) = 1 dx Find y3(1)?

A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)=3 ex cos (yz), Po(0,0,0),…

A: Solution: f(x,y,z) =3exCos(yz) P0=(0,0,0)

Q: Compute the area of the region enclosed x² 5x X 1) y 2 2 2 +

A: