The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing when the length of an edge is 10 cm? (know the formula of surface area of a cube and the volume).

Q: dy Find the complete solution of 2e-2 cosx-sin²x = 0. dx Note: [e"du=e" + C

A: The given differential equation is 2e-2y cos x-dydx sin2x=0⇒dydx sin2x=2e-2y cos x⇒dy2e-2y= cos x…

Q: [²₂1 (²) Given than [ f(x) dx = 3 Ⓒ ® B Lof(² f (x) dx = = [₁, ƒ (² f (x) dx - f (x) dr 1₁° dx -2 3…

A: Given

Q: Find the exact solution for e^2x-6e^x-72=0  If there is no solution NA x=___

A: We have to find the exact solution for  e2x-6ex-72=0.

Q: The selling price P of an item is 100- 0.02x dollars, where x is the number of items produced per…

A:

Q: olve for the general solution using the Power Series. The answer was ready given, you just have to…

A: Please see the below picture for detailed solution.

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

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Q: · ƒ³3(x + 1)(x + 2)²(x² −1)dx with and without the even-odd theorems (show both solutions).

A:

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: If an investment grew to $13,500 in 3 years and the interest amount earned was $1,531.34, calculate…

A: To find out the compound interest.

Q: Cynthia's investment of $81,200.00 in a fund matured to $160,353.29 in 7 years. If the interest in…

A: We want to calculate period and nominal interest rate.

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

A:

Q: A bicycle with 20-inch diameter wheels is traveling at 17 mi/h. Find the angular speed of the wheels…

A: To find out angular speed and number of revolutions per minute.

Q: Let (t) = 5 cos(t) and y(t) = 3 sin(t) All answers should be decimals rounded to 2 decimal places.…

A: Applications of differentiation

Q: True or false If cosh x = then sinh x=

A: We have cheek the statement

Q: 5. Find the limit, if it exists. If the limit does not exist, explain why. sin x- cos x (a) lim x/4…

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

Q: The population of a town is decreasing at a rate proportional to its size. In 1980, the population…

A:

Q: True or false Unlike the anglet in the trigonometric function cost, the t in the cosht represents an…

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Q: Find the area enclosed by r = = √2 sin 0 and r2 = cos 20.

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Q: z²√(-z² + 1)5 dz

A:

Q: The population of a town is decreasing at a rate proportional to its size. In 1980, the population…

A: The population of a town is decreasing at a rate proportional to its size.In 1980, the population…

Q: Find the volume generated by revolving about the y-axis the area bounded by y2= x-2, y=x-4 Use shell…

A: Here we have to find the volume by using shell method.

Q: 4. f(x) = 4x cosh 3x x² ; f'(2.7)

A:

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200…

A:

Q: en fr f(x) dx = √² Iff and g are continuous on [a,b] and f(x) ≥ g(x) for all x € [a,b], then A True…

A:

Q: pair of parametr quations is given. x = e4t y = et (a) Sketch the curve represented by the…

A:

Q: [xv x√2x + 1 dx

A:

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

A: In this question, we want to know whether the given statement is true or false.

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim X x→0+

A: Solution: a) limx→0+sin xx1x2

Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

A:

Q: Find f^-1(x) for f(x) = 9+8x f^-1(x) = ____

A: Topic = Function

Q: 1 -dx= (A) True B) False m 100 8

A:

Q: Given: parametric curve H defined by r(t) = tan-¹t and y(t) = eªt, where t = R (a) Find the slope of…

A:

Q: Find the area of the region bounded by the curve y=x²-3x²-x+3 and x-axis from x=-1 to x=2. (Note:…

A: To find the area of the region bounded by the curve y=x3-3x2-x+3 and x‐axis from x=-1 to x=2.

Q: A sector of a circle has a diameter of 8 feet and an angle of radians. Find the area of the sector.…

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Q: Given x = ; ș¹²+2y — In(y + 1), find the arc length for 0 ≤ y ≤3 8

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: Iff is continuous on [a,b], then [xf(x) dx = x = xf²f(x) A True B) False f(x) dx

A: We will solve the problem

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

A:

Q: e2-s L-1 (5(5²-53) O [(-1/3) + e^(4(t-1))/3] e^2 U(t-1) O [(-1/3) + e^(3(t-1))/3] e^2 U(t-1) O None…

A: We have to find the inverse Laplace transform of the above expression.

Q: 8. For what value of the constants A and B is the function f continuous on (-∞, ∞)? Ar + B for x 2…

A:

Q: FIND THE AREA BOUNDED BY THE PARABOLA x = 8+2y-y², THE Y-AXIS, AND THE LINES y = -) AND y = 3

A:

Q: Find the volume of R using shell method, when R is bounded by y = 4x - x², y = 0 about the line x =…

A:

Q: Find the area of the surface generated when the given curve is revolved about the given axis.…

A: We know that surface area generated when the given curve is revolved about the given axis…

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

A:

Q: Find f. f(t) = f"(t) = 5et + 6 sin t, f(0) = 0, f(T) = 0

A: On solving this we will get

Q: Let x = 11t², y = 9t6 - 2t². d²y Determine as a function of t, then find the concavity to the…

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Q: 3 So² √(√₁² - ²√₁²³) ²³ a dt

A:

Q: Ive what is asked in the following problems. Write your solutions and box your final answer 1. Find…

A: Let's find tangent line and normal line equation.

Q: Determine if the function √x² + y² +1 x² + y² f(x, y): 1 2 is continuous at (x, y) = (0,0). If not,…

A: To find whether the given function is continuous or not at(0,0).

Q: 1 -dx= -2 X A) True B) False 3 100 8

A: