The number of tree species S in a given area A in a forest reserve has been modeled by the power function S(A) = 0.88240.842 %3D where A is measured in square meters. Find S(101). (Round your answer to five decimal places.)

Q: (c) The Cauchy problem u, + Uy = 0, u(x, y) = x on y = 1 has: (A) a unique solution (B) no solution ...

A: Given

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Q: Exact Equations (w³ + wz² – z) dw + (z³ + w²z – w) dz = 0 O (w² + z?)² = 4wz + c O (w? + 2?) = (4wz ...

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Q: Consider ſ* xe-**dx. What will be the appropriate solution and answer to this improper integral? lim...

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Q: Find the solution of the following equations: 1. у' —х-4ху 2. (2xy + x² + x+) dx – (1 + x²) dy = 0 3...

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Q: x + 3 b. a. 1 = x + 1 c. Vx + 16 =x + 4 %3D с.

A: Given: -The statement is, for the counterexample, (a). xx=1 (b). x+33=x+1 (c). x2+16=x+4 To verify: ...

Q: Find range of function f(x): b) f(x)= (2 – x)V 4x – x²,xE (0, 4) -

A: b)   f(x)=(2-x)4x-x2 , x∈(0,4)         plot the function on the graph    

Q: Evaluate the integral: I = 2x S where the solid S is defined as: S = {(x, y, z) E R³ : x > 0; 0 < y ...

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Q: Given that - 3| de k then the value of will be given by В. 13 10 C.I D. 14 E. None of the given choi...

A: We will find the value of k  in the following step.

Q: u du Form Answer Ex. S 3+ 2cosx 5sinx 5 -5V3+ 2cosx + C dx 3+ 2cosx -2sinxdx ī du 3 15. Given: S -dx...

A: This is a integration problem

Q: find the area of the region bounded above by the curve y = 2e^-x + x, below by the curve y = e^x/2, ...

A: To find the area of the region bounded above by the curve y=2e-x+x, below by the curve y=ex2 on the ...

Q: O A) (-1, 1) B) (-o, - 2) U (0, 2) O C) (0, co) O D) (-o, 0)

A: A function f(x) is decreasing on [a,b] if the graph f'(x) is moving downwards on [a,b]

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Q: Find an equation of the tangent line to the graph of the function at a given point. Note: You may/ma...

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Q: I have 1 yard piece of fabric with 45 inches width. I am planning to make hand towels out of it. If ...

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Q: Find dydx for y=ln2x3−x2

A: This question is based on derivative.

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) x2 n- 4, c-2 P4(x) -

A:

Q: 9. Evaluate the integral ex V2e-2x – 3e2x 2/2e-2x – 3e2x +C А. 1 3eªx – 2+C B. 2/3 Arcan V3e2x Arcsi...

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Q: e2t+a (2 cos at – 3 cosh 2at) -

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Q: 00 k k 2. Σ (- 1)- k+1 k=0

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Q: when r = 5 and dt An expanding sphere has radius r = 0.6t cm at time t (in seconds). Let V be the sp...

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Q: 11. The integral of an(In|4x=12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. С. 4 D. I

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Q: csc x du (3T 5. If u = f(x), then dx sin x – cos x Compute f и %3D (a) 1 (b) -1 (c) 0 (d) 2

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Q: Find the average rate of change for the following function. f(x) = 2x - 5x +3 between x = - 1 and x ...

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Q: Use the shell method to set up a definite integral (set up only, do not evaluate the integral) for t...

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Q: 5. Consider the function below. Is g continuous on (0,1]? on (4,1)? Why or why not? if x 4.

A:

Q: x3 + 3x2 + 4r +1 dx (r2 + 2x + 2)2

A:

Q: Evaluate the integral cot 2x dx cot2 2x - 15 -금사 csc 2x +C A Arcsec 4 B -In/cot 2x + cot? 2x – 15|+C...

A: Here, the given integral is: I=∫cot 2xcot22x-15dx

Q: 0 Use an appropriate form of the chain rule to find dw/dt w = 5x²y°z*; x =², y = t², z = t°

A: As per our guidelines, we only solve one question.

Q: One of the following is an improper integral. cln 3 e* dx dx J, xV16 – In x In 2 V4 - ex In 2 CA dx ...

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Q: Illustrate the Quadratic Funictions Using table of Values Think About This! Consider the table of Va...

A: Quadratic

Q: dx The integral can be rewritten as -∞ V1 – x (a) lim (-2+2vī1-s) (b) lim (-1+ 2v1 – s S--00 S--00 (...

A: Given ∫-∞0dx1-x Let t=1-x differentiating with respect to x, dt=-dx ∫-∞0dx1-x=-∫-∞0dtt=-∫-∞0(t)-1/2 ...

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Q: Given: x² dx Find: Formula So"du Sa"du

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Q: Find the laylar polynomials of orders = 0,1,2,3, and 4 about x = No, and then find the nth laylor po...

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Q: Suppose a sample of a certain substance decayed to 73.6% of its original amount after 300 days. (Rou...

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Q: 1 dx. 10. Evaluate the improper integral m 64 + z²

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) n = 4, c = 4 Pa(x) =

A: see below the answer

Q: du Form Answer u 10 20. Given: Tdx a) 3 a" du Find: formula b) | a"du c) a"du d) a"du

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Q: y(x^2+y^2-1)dx+x(x^2+y^2+1)dy=0 solve the differential equation

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Q: In3 in2 4-ex xp- xV16-Inx 1 x Vinx In2 iv. Ino.5 e2x +1 1 O 2/22 O8-2/15 O 3 2 OIn 2

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Q: Find F. dr, where F = 3yi – 8x3+ (8y – 8x)k and C is a - circle of radius 8 in the plane x + y + z =...

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Q: Find the radius of convergence and the interval of convergence. k(k + 1) k=1 1) First apply the Rati...

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Q: Evaluate the integral dx 2xx - 3x?

A: To find: The integral ∫dx 2xx3-3x23 Concept used: ∫1-v2+1dv=lnv+12-lnv-12

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) In(x), n = 4, c = 3 PĄ(x)

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Q: Find the nth Maclaurin polynomial for the function. 4x – 4 f(x) = n = 4 %3D X + 1 Pa(X) = || %3D

A: Here, the given function is: f(x)=4x-4x+1      =4x+4-8x+1      =4(x+1)x+1-8x+1      =4-81x+1

Q: Evaluate the integral S dx 2x3 - 3xx 1 -In 2/2 "I/3x + /2 +C En(2 { x³ - 3x x)+c 1 V2 + V3x -In + C ...

A: First we take common x3/4 then put√x=t  And using integration of 1/a2 - x2

Q: 7Q b) TR = (Q+3)

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Q: 1 |dz 4z

A: