DEFINITE INTEGRALS Evaluate each of the following definite integrals: 21. ²(6x² + 3)dx 22. (4x+1)dx

Q: 3.) Using the Graphing method, find the limit. When necessary, state that the limit does not exist.…

A: Solution is given below:

Q: For each of the following functions, find the derivative (dy/dx) with respect to x: 7. y = cos x 9.…

A: The given functions 7. y=cos x8. y=ex9. y=ln x we have to find the derivative of this functions.

Q: y C (0,4) O R₂ y = 4√x R3 y = 4 x R₁ B(1,4) A (1,0) X

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Q: 1. (Difference Quotient) Simplify the difference quotient (x+h)-f(x) for each of the following…

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Q: 6 5 4+- 3 2 1 1 +- I lim 1-8 lim lim → 4¹ 1 0 1 2 y = f(x) →4 T T I T 1 Enter each answer as a whole…

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Q: Function h(t) = sin t + et Point 1 Let (₁1¹) (ㅠ, 6 (a) Find an equation of the tangent line to the…

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Q: A, B, and C are mutually exclusive events and P(A) = P(B) = and P(C) ½, "(B'n c'). = find

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Q: Find ¹ 2 2x² ке 22 дуг Z=109 √√x²+² xy

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Q: Complete the table. (Round your answers to five decimal places. Assume x is in terms of radian.) 5…

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Q: The radian measure of an angle of - 218 degrees is

A: For the given problem We can change degree into radian

Q: Find the domain of the function. (Enter your answer using interval notation.) √x 8x² + 7x1 g(x)= =

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Q: 1. Determine the derivatives of the following functions (a) y = (x² - 2)²

A: We can determine the derivative in the below steps.

Q: Find expressions for the quadratic functions whose graphs are shown. f(x)= g(x) 11 y

A: Given :   f(x) Vertex ( h , k ) = ( 7 , 0 ) put point ( x ,y ) =( 8 , 2 )

Q: quart is 25 percent of what measure?

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Q: make

A: We have to find the following conditions according to the given information

Q: Find the integral. (Use C for the constant of integration.) 9 J 49x2 dx

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Q: Given the graph of f(x)=√x as shown, graph the function -4f(x-4). -8 -7 -6 -5 -4 -3 -2 -1 8+ 7+ 6+…

A: We can graph the function asked using the given data.

Q: 1337 (2) =?

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Q: Find the x- and y-intercepts of the graph of the equation. (If an answer does not exist, enter DNE.)…

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Q: Use Green's Theorem to evaluate 90 O O -384 O -48 fayd r²y² dr + (yr³+ y²) dy where C' is shown…

A: As we know from Green's theorem: ∫cMdx+Ndy=∫∫R∂N∂x-∂M∂ydA Where, ∬dA=∬dxdy or ∬dydx And We know the…

Q: (a) Find the Taylor series expansion of the function et around x = 0 (b) Use the series above to…

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Q: 1. The population of a city is growing by the same percent every year. The population at the 2000…

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Q: 14. F(x)=sin(t²)dt. [sin(t²)dt . Find F '(1). O 0.292 0.540

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 27. A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is…

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Q: mplete the description of the piecewise function graphed belo 6+ 5

A: Here we have to complete the description of the piecewise function graph below.

Q: Prove that tan'z= leto 1/2 in (1+2) tan't z • tanw=Z Z = Sinw cosw

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Q: (3) Find the radius of convergence of a) infinite b) 1 not defined 0 infinite X Σ₁ F

A: The given series is: ∑j=1∞xjj2 Let, aj=xjj2; j≥1

Q: Graph on a cordinate plane by hand or a graphing device 2x-3y=18 3 -X -x + ²y = 8 zy If there is one…

A: The given equations, 2x-3y=18-x+32y=8

Q: C. Find the standard form of the equation of a circle given the following conditions. 11. Radius is…

A: To find the standard equation of the circle given the following conditions.Radius is 5 and passes…

Q: A bicycle tire inner tube producer can sell 1111 inner tubes at a price of $1.54$⁢1.54 per inner…

A: Given problem:- A bicycle tire inner tube producer can sell 11 inner tubes at a price of $1.54 per…

Q: Use Green's Theorem to evaluate >[2²y² dz + (yz²³ + y²) dy where Cis shown below. 90 O-384 O-48…

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Q: 2. Show that the function f(x) = xsinx has in infinite number of Critical Points by doing the…

A: The given function is : f(x)=xsinx Now finding the derivative f'(x) :

Q: A) x4-(y-1)4 lim (x,y)→(0,1) x²+(y-1)² = 0

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Q: If you count from 10 to 120, how many 5's will you find along the way?

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Q: 4₁ An online company lets you download songs for $0.99 each after you have paid a $5 membership fee.…

A: 4. An online company lets you download songs for $0.99 each after you have paid a $5 membership fee.…

Q: A. Write ✓ on the line if the given equation is a circle; otherwise write x. If the equation defines…

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Q: A piece of rectangular sheet metal is 24 inches wide. It is to be made into a drain gutter by…

A: We have to find the value of x that gives greatest capacity.

Q: (-5, 3) 6 T ? cy 7 O T 4 ? T (0, 0) Return this question to its initial state On the graph, make the…

A: This is a problem related to line equation. Please follow the procedure given below.

Q: 2₁ The graph below models the height of Sam's kite over a period of time. Explain what the zeros of…

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Q: Solve the diff eq. (Homogenous) y' = ysecx

A: The given equation is: y'=ysec x⇒dydx=y sec x⇒dyy=sec x dx

Q: How are you getting a negative for a and where is the equation coming from for b?

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Q: 3. dy + dx x² (y² + 3) y (x³+1) = 0.

A: Here we have to solve the differential equation.

Q: 5. Find and sketch the domains of the functions of two variables below. Sketch the boundary with a…

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Q: a. f(x)=x-1 x²+1 b. fx=CSCTX

A: To find the vertical asymptotes , put the denominator equal to zero and solve for x.

Q: A water container has an open top and is accelerating at a = 4.4 m/s² along a slope with an…

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Q: 10- x - x² if 3x + 13 if In(x-1)-2 if Calculate the following limits. Enter "DNE" if the limit does…

A: Topic - limits and functions

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Q: The function f is continuous where f(-5) = -1 and f(5) = 6, and g is a function defined by g(x) = 1…

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Q: Q3: Solve the differential equation subjected to the condition y(e)=e² and give the result in…

A: Let's solve given differential equation.

Q: Below table contains position-time data for a runner during the last 0.25 s of a 100 m sprint. Time…

A: Given: table is given in the question we have to find the value of acceleration at 99.44 meters