Find the domain of the vector function r(t)=⟨ln⁡(19t),sqrt(t+8),1/sqrt(7−t)⟩ using interval notation.

Q: Let F(x, y) = 1+ 4 – y². a. Evaluate F(3,1). b. Find the domain of F. c. Find the range of F.

A: Given:

Q: Write an equation of the tangent line to the curve f (x) = 3//a + 8x at the point (4, f (4). Upload ...

A: We have to calculate slope of the tangent

Q: Find the equations of the line through (2,0, –4) and parallel to each of the planes x + y – z = 0 an...

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Q: 3 2t + 3 h(t) = 6 t2 Find h'(t) *

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Q: 1. =2*e* = 2*e*

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Q: 1. Find the limit of the following: х* — 11x5 + 37x* +6х3 — 297x? + 621х — 405 - lim,-3 А. x→3 x° — ...

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Q: Find the open intervals on which the function f (x) = x + 6v4- r is increasing or decreasing. If the...

A: Solved below

Q: dx Evaluate the given function : Vä(1+væ)

A: Here we have to evaluate the given integral.

Q: Evaluate the integral below along the given path. (Give your answer correct to 2 decimal places.) C:...

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Q: . Use the appropriate limit laws and theorems to determine the limit of the sequence. an=(3+8/n^4)^1...

A: We will evaluate all above as shown below

Q: d) Graphs of the revenue and cost functions are shown below. Answer the following questions. R(x), C...

A: topic- functions 

Q: 1. siny dx + (x - sin? y)dy=0

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Q: 8. fx,y) = sinx cos y

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Q: For function, find the point in the graph at which the tangent line has slope 9 Y= -0.025x^2+6x What...

A: The given function is:Y=-0.025x2+6xThe slope is 9

Q: In Exercises 7- 12, functions z = f(x, y), x = g(t) and y = h(t) are given. dz (a) Use the Multivari...

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

Q: the arm of a ferris wheel starting from the center to its passenger seat has a length of 80 ft. how ...

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Q: Solve for the derivative Arc sin + Arc cos =0 y y

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Q: Evaluate the following limit using L'Hospital's rule. :- e13z lim 5x2 – 11x + 8

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Q: The function below is continuous at every real.number. Find the value of (m + 3/2). 1– 2x if x >4 mx...

A: We have to find 

Q: The function f(x) = 2/(x-5) is continuous on the interval (0, 5). Select one: O True O False The fun...

A: Answer: false

Q: Find the sum of the infinite series, if it exists. -16 -64 32 8, , 5, 27· 3 Enter the sum as a fract...

A: The given infinite series,8, -163, 329, -6427,.......

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. ...

A:  A sequence an is convergent if it has a unique and finite limit "a".And we say that the sequence is...

Q: 3 x° +x* dx x² 4 3

A: The given integral is solved below in detail.

Q: The point P (3,-8) lies on the curve y = x2 - 8x + 7. The point Q (x, x2 - 8x + 7) is also on the cu...

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Q: / (3cosh m 2 cosh m sinh mdm +e°

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Q: A. Find the differential equation: (1) whose general solution is y = c,e-2x + cze3x (2) by eliminati...

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Q: find the equation of y where dy/dx = 3x + 5 and y= 6 when x = 0

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Q: Verify that the area under the curve y = 1/x from x = 1 to x = m equals 2m, the area from x = 3 to x...

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Q: Evaluate dy/dx at x = 2.5, correct to 3 significant figures, given y= (2x^2+3)/In 2x

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Q: Variable Separable (6) (xy - 3y + x – 3)y' = xy + 2y – x - 2 (7) y' kM – ky; Provide the explicit so...

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Q: Show that In x lim x→1 x – 1 1.

A: To prove: limx→1 ln xx-1 =1 limx→1 ln xx-1 =00 form L'Hospital's Rule tells us that if we have an in...

Q: Evaluate the integration by part

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Q: Evaluate f"(e) when e = 0 given f (e) = 2 sec 30

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Q: If f(x)dx=6, | f(x)dx=2, and] f(x)dx= - 3, find / f(x)dx. B 3.

A: Given query is to find the value of the integral.

Q: Q = 6x + 3xy + 2y

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Q: Homogeneous ODE x^2y'=4x^2+7xy+2y^2

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Q: Question 14 (1 point) Find the limit of the infinite sequence. 2, 2, 2, 2, 2,. Enter dne if the limi...

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Q: Homogeneous Differential Equations (13) (4x* + x³y + y*)dx + x*dy = 0

A: We are asked to solve the homogenous differential equation   

Q: to, thenk is15 not a - andly-k) 5/15 not a If fQ) =0,thvnk 5/5 not cs ond Oxok) Is/15 not a

A: The Remainder theorem says that if a polynomial P(x) is divided by (x-a) then remainder obtained is ...

Q: Consider a circle with equation x² + y² = 20 and the point P with coordinates (-1, 2). Is P inside, ...

A: We have to solve the circle inside, outside, or on circle

Q: 3- 2-6 -3 -2 -1 1 2 3 The following function is discontinuous at three values of x. List these value...

A: We will find the point of discontinuity. 

Q: edxte*

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Q: . Determine whether the given sequence converges, and, if it does, find the limit. i. an = sin ii. a...

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Q: Evaluate the given function ſ sec5xtanxdx a. sec*x + C b. sin*x + C c. cosx + C d. 금esc5x + C

A: topic - indefinite integral

Q: A grain silo consists of a cylindrical main section and a hemispherical roof. If the total volume of...

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Q: . 2yda + (x – x³y³) dy = 0

A: here we have to check whether the differential equation is exact or non exact.

Q: Given the differential equation d?y 12. + 4y = 0 di? Determine the Characteristic Equation for the g...

A: We have to find characteristics equation

Q: Prove the following indentity. - 1 attachment - sece sine = cot0 sino cos0

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Q: dt 15+2t-t

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Q: |The vector projection of v = 4î + 4j + 4k onto W = 5î - 4ĵ + 3k is aî + bî +cê: where the exact num...

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