How many ways are there to represent a function? Find the domain of the following function x²+3x+1 V2x-1 Vx-1 i. f(x) = ii. g(x) %3D %3D x2-1

Q: The present value of a sum of money is the amount that must be invested now, at a given rate of inte...

A: topic - present value 1year =52 weeks

Q: The radius of a circular puddle is growing at a rate of 15 cm/sec. (a) How fast is its area growing ...

A: Given :-  dr/dt = 15cm/sec  a) how fast its area growing when radius is 30cm  b) how fast its area i...

Q: Find the Taylor polynomial of degree 3, centered at a 3 for the function f(x) I+ 4.

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Q: Find the Laplace transform of the function ( 3, 0<t<5 ( 0, st<0 f(t) NOTE: Express the answer in ter...

A: Laplace transform

Q: 1. A strictly monotonic function is defined as a function that either always increases or always dec...

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Q: Evaluate the integral of the improper fraction using partial fraction method - 2x + 6 + 1 d. 2x-8

A: We have to find given indefinite Integration.

Q: The area of a circular sunspot is growing at a rate of 700 km2/sec. (a) How fast is the radius growi...

A: Question:The area of a circular sunspot is giving at a rate of 700 sq.km/sec  a) how fast is the rad...

Q: For the cost function, find the marginal cost at the given production level x. State the units of me...

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Q: If $1500 is invested at an interest rate of 3.5% per year, compounded continuously, find the value o...

A: topic - exponential function

Q: 3-1 4. The value of the indeterminate form from lim is 1 4r2 - I- 3 (a) 0 (b) 00 (c) 1 (d)

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Q: 25. f(x) = 1 – V

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one. ...

Q: Determine the value of x of the discontinuous function: * x – 1 x 3

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Q: C) Replace the following polar equation by equivalent Cartesian equation. rsine Inr + In cose %3D

A: We can replace the given polar equation by equivalent Cartesian equation as below.

Q: dx Evaluate -1 x2 - 0 -2

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Q: A table of values is given for a function f(x, y) defined on R = [1, 3] × [0, 4]. 1 2 3 4 1.0 2 -3 -...

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Q: (2.13) Compute Lp(t), where P is the regular tetrahedron with vertices (0,0,0), (1,1,0), (1,0,1), (0...

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Q: *tan(e-x) Given: et Find: du e*dx O -e*dx O -e-*dx e-*dx

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Q: sin 6z Evaluate: lim エ→0 00 O1 Which among the following limit theorems were applied? sin x O im エ→0...

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Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density ...

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Q: sec3(In x) + sec²(In x) tan(In x) dx Given: 2x Find: du V sec (In x) + sec²(In x) dx tan(ın x) dx ta...

A: On solving this we will get

Q: Using diliferentials, determine the appropriate O a. 47.1 cm3 Ob.314.2 cm3 OC 15.7 cm3 O d. 539.5 cm

A: Given query is to find the the change in the volume of sphere.

Q: lim x→0 4-Vx+16

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Q: Identify whether the statement represents an exponential function. For each training session, a pers...

A: Topic:- function

Q: Csc- X S- /cor?(x)- acot(=x) + 4 Given: dx cot(슬x)+.

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Q: Question 1 Find the derivative and simplify y cotVt-1 Oy-- Oy= - 2tt-1 1 2t/t-1

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Q: SV1+ vw_dw

A: ∫1+wdw  

Q: In3 ex i. dx In2 4- ex i. X/16 - Inx e 1 iI. i xInx In2 1 dx Ino.5 e2x + 1 iv.

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Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show ...

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Q: The graph of an everywhere differentiable function is shown below. Use it to select the correct ineq...

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Q: sec? x dx- 4 Evaluate /1-tan x O-1 O -2 1 O 2

A: We have to find the integral

Q: Use Lagrange multiplier to solve. Max U = x+y+z subject to xyz = 8

A: max U=x+y+z subject to xyz=8

Q: 1 8. If y = 1+ a) Prove that y' = 0. b) What kind of functions have derivative 0 ? c) You can actual...

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Q: Use sigma notation to write the Taylor series about x = xo for the function. e; xo = 10 O 00 e10 E* ...

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Q: Calculate (1+ cos(y²))dA,where D is the triangular region with vertices(0, 0). (–2 - Vĩ,2· VT) e (0,...

A: Given problem:-

Q: sec (In x) + sec2(In x) tan(In x) 2х Given: dx Find: du tan(in x) 2х sec³(In x) + sec²(In x) sec(in ...

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Q: 14. Find dr/de: r= 0 sin 0 + cos 0 а. cos @ b. 0 cos 0 0 sin 0 C. O a O b

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Q: 3. y³x2 – cos- sin x² + esin x = 1 y DIFFERENTIATE THE GIVEN

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Q: Find the point on the plane 2x+7y+8z-14 =0 closest to the point (-3,3,1). The point is (Simplify you...

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Q: dx Given: 2x- 3xlnx Find: du dx 3 dx dx 3 dx ---

A: Explained below 

Q: A 12-lb weight stretches a spring 2 ft. The weight is released from a point that is 1 ft below the e...

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Q: The cost function for a certain commodity is C(q) = 87 + 0.14q − 0.007q2 + 0.0002q3.   (A)  Find  C ...

A: The cost function for a certain commodity is C(q) = 87 + 0.14q − 0.007q2 + 0.0002q3

Q: A paint store sells 270 pails of paint per month at a price of $32 each. A customer survey indicates...

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Q: Find fo g, g o f, and g o g. f(x) = 2x, g(x) = x4 %3D (a) fog (b) gof (c) gog

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Q: Which among the following is an improper integral? 1 A x[In?(3x) – 4] Inx x[In*x- 1] ` .0.5 1 dx -0....

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Q: Determine the value of x of the discontinuous function: х — 1 f (x) 3D {3х — 3 (-4x + 3 x 3 -

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Q: || x? zdS, where S is the part of the plane z = 1 + 4x + 3y above the S. Evaluate rectangle [0, 3] x...

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Q: The function f is defined as f(x) = (x – 3)(x + 6)². Answer the following questions without using a ...

A: The given function,      fx=x-3x+62

Q: One of the following is an improper integral. Determine which one it is then evaluate it. What is th...

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Q: The sum of one number and three times the second number is 48. What will be the maximum product of t...

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Q: S2x°(3- 5x*)'dx Given: Find: Formula 10 Judu Sudu 2 fu'du -2 fu' du

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