3. Use the limit definition of the derivative to find the derivative of the function. a) f(x) = 2x² + 3

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A: First we rewrite the profit function in terms of t.Then differentiate p(t) with respect to t.

Q: Ussing the Simpson Is rule, find the followmy integrals. A=2 zolnہوم @

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

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Q: x² dx -1 (2x²+2x+1)² sº₁

A: We have to evaluate the integral. ∫dxa2+x2=1atan-1(xa)+c

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A: We have to find the composite function.

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Q: Find the length of the are of the function x² = 4y from x = -3 to x = 3.

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Q: Which of the following statements about the graph of f(x) = (2.25) shown above are true? Select all…

A: Given graph of f(x)=(2.25)x

Q: Topic: Arc Length Find the length of the arc of the function x^2 = 4y from x = -3 to x = 3. a) Graph…

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Q: 1) Find the radius of convergence and interval of convergence of the series. Show All Your Work.…

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Q: 2 cos x = -0.7, 2TT ≤ x < 4T csc x = 2, 0 < x < 2TT sec x = -3, -π ≤ x < T 4

A: Given :cosx=-0.7cscx=2secx=-3

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Q: 11. Find the limit using algebraic techniques. The limit of f(x) = -4 O- 0 O=¹ x+4 2x²+5x-12 as x…

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Q: 3. f(x)= x² + 3

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Q: 1. Evaluate the given integral Q. J[(y - 2x) dA, R where is the region bounded by x = 0, y = x, x =…

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Q: Find the integral offsec²x dx tan x

A: This is a problem related to integration. based on the general formula and concepts we will answer…

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Q: 32/5 y=x² 32 Find the area of the region bounded by the graphs of y = x² and y = 4x. 64/3 32/3 64

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given…

Q: 3. A spherical balloon is inflated at a rate of 100 cm3 /sec. How fast is the radius changing when…

A: We know that volume of the balloon is V=43πr3                          (1) Given that Spherical…

Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

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Q: dw For the functions w= -5x² + y², x = cost, and y = sint, express as a function of t, both by using…

A: Given query is to find the Indicated derivative.

Q: Find the slope and the rate of change of the slope with respect to x when t = 90°. x = 2 cos (3t)-3…

A: This question can be solved using the concept of first and second order derivatives at t=90°

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Q: -3x² - 4x + 3 1 x (x + 1)² dx

A: Given problem:-

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Q: For each given functions, find the slope of the tangent at a given point using first principle…

A: We have to find the equation of tangent.

Q: S 10dz 4z3-4z²+5z

A: To evaluate the given integral:

Q: (e) ƒ(x) = x³ (x + 5)²

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Q: 2. Consider the function f(r). 2r²-9r-18 r²-r-2 (a) Sketch the curve y = f(r). (b) Find the area of…

A: We have to sketch the curve and find area.

Q: Setan2 sec² 2xdx Select one: O a. 0.4325 O b. 0.0287 O c. 0.6543 d. 0.0177

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Q: Solve the initial value problem 2y" + y' - 10y = 0 y(0) = 0 y'(0) = 1

A: We have to solve the initial value problem.

Q: 17. What is the amplitude of the graph y = -4sin (x - 2)? The amplitude is. units. 04 02 O 2T O K|N…

A: For the equation  y=A sinBx+C+D   A-  Amplitude   B- Frequency   C- Horizontal shift   D-  Vertical…

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Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: Ths question can be solved using the formulas of Laplace transform.

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Q: 3. Determine the limit graphically. Confirm algebraically. x - 1 lim x-1 - 1 1² - 3t+2 lim 1-2 1² 4…

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Q: If repetition is not allowed, in how many ways can we arrange ♣, ♠, ♦, and ♥ a) four at a time? b)…

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Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

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Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² +1 a. (3,4) b. (0,3)…

A: To find the linearization Lx, y of the function at each point.fx, y=x2+y2+1 a 3, 4b 0, 3

Q: 2. Use integration to find the volume of the solid generated which is bounded by x + y = 2 and the x…

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Q: In how many ways can a committee of 5 people be chosen out of 9 people?

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Q: Evaluate the equation for f Select one: a. 0.5 b. -1 Oc. 2 Gd. 1 dzdy

A: Let I=∫01∫yy21y2-x2dxdyLetI=∫01(I2)dy                                    (1)WhereI2=∫yy21y2-x2dxWe…

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Q: The cost in pesos of manufacturing x pairs of pants in ABC Tailoring is given by C(x)=1500+3x+x^2…

A: