Find the indefinite integral and check the result by differentiating. [2x (x²+3) ºdx 9 [2x(x² + 3)dx=

Q: 4) Let R be the region in the first quadrant bounded by the graphs of y=√ and y= a. Find the area of…

A: As per the guidelines we are supposed to solve only the first 3 subparts only, so please upload…

Q: 2. Find the derivatives of the following functions. (a) f(x) = e sec x

A: We have to solve the derivative of the given function.

Q: (23) Find the volume of the region beneath the surface z = xy + 10 and above the region between the…

A: z=xy+10

Q: The joint cost, in dollars, for two products is given by C(x, y) = x²√√y² + 11. (Round your answers…

A: The joint cost is given as , Cx,y=x2y2+11

Q: A 4th-degree polynomial function has zeros at 3 and 5-i. Can 4+i also be a zero of the function?…

A: 4th degree polynomial function has zeros: 3,5-i

Q: •√√x 2 0 x² +1 -dzdydx

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Here  point P (-3,1,5) and A(1,1,0) and B(-2,3,-4).  We find distance.

Q: Exact Differentail Equation M (x,y) dx + N (x,y) dy = 0 is an Exact DE when ∂M/∂y = ∂N/∂x Solution…

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Q: Question 2 Find y' given 2 + x¹y² = y sin¯¹ y²

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Q: Question 6 Find the error in the measurement of the area of a rectangle if the error in the…

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Q: Mixing the Fuel Having finalized the container, you are notified by your computer that you need to…

A: To find the stabilization level?

Q: The population of a bacterial culture was 5000 bacteria after 15 min and 40 000 bacteria after 1 h.…

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Q: The velocity (in feet/second) of a projectile t seconds after it is launched from a height of 10…

A: Given that the velocity of a projectile t seconds after it launched from a height of 10 feet is…

Q: 8. Given f = {(1, 4),(2, 5),(3, 3),(4, 2)}. Find the following: a) Find f(4): Answer= Undefined b)…

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Q: Find the equation of they hyperbola with center (6,1); vertices at (4,1)(8, 1); and foci at (0, 1)…

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Q: Use the ratio test to determine whether an+1 (a) Find the ratio of successive terms. Write your…

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Q: Find the tangent plane of f(x,y,,z) = 30 -x2-y2-xyz at x=3, y=1, z=-7

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Q: Given that f(x) = 7x - 8 and g(x) = 1 - x², calculate (a) f(g(0))= 0 (b) g(f(0))=

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Q: 49. Find a > 0 such that the tangent line to the graph of f(x) = x²e¯x at x = a passes through the…

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Q: 29. f(x)= = ex+1 +x 2ex - 1

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Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

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Q: 2 5 If the directional derivative value (Duf) of the function f(x,y) = x²-3x4 + 4y at Point (-2,0)…

A: Let (u) = Ai + Bj be the unit vector in the direction of the directional derivative at the point…

Q: 3=e4x +1 a) .693 b).234 c) .1732 d) .205 e) 0.67

A: 3=e4x+1

Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

A: To find out the maximum and minimum.

Q: You are driving away from home. At noon, you are 47 miles away. Your velocity (miles per hour) away…

A: We have to find the total distance travelled at speed of vehicle at 3 pm.

Q: You are standing above the point (2,5) on the surface z = 30 - (2x² + 2y²). (a) In which direction…

A: z = = 30 — (2x² + 2y²).

Q: Frequently, we encounter a need for two (different) linear transformations to Transform a…

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Q: Blood Alcohol Level The percentage of alcohol in a person's bloodstream t hr after drinking 8 fluid…

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Q: If C(x) = 15,000 + 400x - 2.8x² +0.004x³ is the cost function and p(x) = 4,000 - 7x is the demand…

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Q: A robotic machine fills containers with an acid solution at the rate of 120 + 4t milliliters (mL)…

A: Rate of Change of acid solution (in mL/s ) :

Q: 18) A sports company has the following production function for a certain product, where p(x,y) is…

A: Given: p(x,y)=2000x45y15wherep(x,y) is the number of units produced with x is the units of labour…

Q: The monthly sales of a certain widget are expected to increase at a rate of S'(t) =   2et   3 + et…

A: The monthly sales of a certain widget are expected to increase at a rate of  S't=2et3+et widgets per…

Q: Use the graphs of f, f', and f" to estimate the x-coordinates of the maximum and minimum points and…

A: Solve the function

Q: Use Theorem 2.1.2 to find the slope of the tangent line of f-1 at x = sqrt3 / 2. Given f(x) =…

A: The given function is f(x)=cos⁡(3x)   To find: (f−1)'32=?

Q: Using the properties of combinations of continuous functions, x2−5x-6 determine the interval(s) over…

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Q: A can buoy is to be made of three pieces, namely, a cylinder and two equal cones, the altitude of…

A: A can buoy is to be made of three pieces, namely, a cylinder and two equal cones, the altitude of…

Q: QUESTION 8 The terminal point determined by t is O O b. O C. sin t = sin t = sin t = 7 3. 3 COS t =…

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Q: 33. Let g be the inverse of f(x) = x³ + 2x + 4. Calculate g(7) [without finding a formula for g(x)],…

A: Let g be the inverse of fx=x3+2x+4.

Q: A cylinder shaped box with no top has a fixed volume of 87. Find the radius of the base and the…

A: Given: A cylinder shaped box with no top has a fixed volume of 8π. We are required to find: Radius…

Q: Compute the double integral y dA over the domain D indicated as 0≤x≤ 4, x ≤ y ≤ 3x + 5. (Use…

A: Solve the following

Q: Creating the Fuel You now have the bacteria needed to create the fuel. "Computer, what is the next…

A: We have to use the concept of differentiation

Q: 1. Fill in the chart. f(x) ex ax In x f'(x) f(x) arctan r arcsin x f'(x)

A: We need to find the given derivatives:

Q: 7/2 cosesino drde

A: We need to solve the given double integral.

Q: The graph below shows solution curves of the differential equation dy 4 1/3 3 Find an equation for…

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Q: Suppose that the value of a yacht in dollars after t years of use is V(t)=300000e^(−0.12t). What is…

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Q: For what values of a does the series A (В C D x = only 8 1 < x < 2 only 1 ≤ x ≤2 only n=0 (2x - 3)"…

A: The given series : ∑n=0∞2x-3nn!.We need to determine the values of x for which the series converges.

Q: 2x x - 3. a) Find the domain of the function: [-3, ∞0) (-∞0, 3] (-∞, 3) U (3, 0) (0, -3) U (-3,0) 2.…

A: According to bartleby guidelines we supposed to do the first subparts of multiple subparts kindly…

Q: Use the properties of logarithms to rewrite and simplify the logarithmic expression. log3(92.24)…

A: let  M=log392.24from properties of log function (i) logaa=1(ii) logxn=nlogx(iii)  loga.b=loga+logb

Q: Use the remainder theorem and synthetic division to find the value of f(2) for f(x) = 2x3³-4x² +85…

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Q: What is the remainder when 4x³-4x²+1 is divided by x-2? O 17 Оо

A: Given 4x3 - 4x2 + 1 divided by ( x - 2 )