Given x = 2 lnt and y = 1+t, find the equation of the tangent line when t = 2. %3D O y=-4x-8ln(2)-5 O y=4x+8ln(2)+5 O y=4x+8ln(2)-5 O y=4x-8ln(2)+5

Q: For what values of x is fAx) increasing if f '(x) = 3-х (2r – 9)(x +4) %3D

A: We have to find the value of X in the function in which function is increasing.

Q: (j) lim sin z I→0+

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Q: What type of critical point is located at x =-6, if ƒ '(x) = (x – 2)(x + 6)?

A: This question is based on application of derivative.

Q: Find a formula for the nth term of the sequence 1, - 4, 9, – 16, 25, ..

A: We can find the nth term of the sequence. We notice pattern of the sequence.

Q: ppose a compa headsets, the cost and revenue functions (both in dollars) are given by C(x) = 32,000…

A: Profit = revenue - cost Px=130x-0.001x2-32000+60x=-0.001x2+70x-32000

Q: To evaluate f dx, we choose : ,dv = xdx b)u = Vx - 1, dv = x dx %3D du

A: ∫xx-1dxLet u=x-1.=∫ 2u2+1du=2·∫ u2+1du=2∫ u2du+∫ 1du=2u33+uSubstitute back…

Q: Question 2 ) Consider the initial-value problem y" + 4y = 5 sin 3t, y(0) = 0, y(0) = 3. %3D (a) Use…

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Q: The solution set of non-negativity constraints is located at Y-axis Quadrant II 3- QuadrantI X-axis…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx, Po(3, - 3,…

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Q: x2 + 7x – 3 | dx J (2x + 1) (x – 2)²

A: Given problem:-

Q: -2 is a critical number of the function f(x) = /2x - x2, Select one: O True O False

A: The given function is  f(x)=sqrt(2x-x2)

Q: 1. Find the total differential dw. 2. w = re2u +e-V

A:

Q: Which of the following is the particular solution of a nonhomogeneous differential equation…

A: Here, given that: yc=c1x2+c2x3⇒y1=x2, y2=x3 And, u1=2x-3x2, u2=2x+3

Q: (iv) 15-22 dr. u = (v) S 15 · T/9 – x² dx. 9-z (vi) J +15 da. u=

A: iv) 15x2/sqrt(9-x2) v) 15 pi sqrt(9-x2) vi) 9x/(x2+15).

Q: 15. Determine the coordinate of point C, which lies on the y-axis, if it is equidistant from point A…

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Q: Find and sketch the domain for the function. f(x.y) = / (x - 9) (² - 4) Find the domain of the…

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Q: 1. Find the inverse of the matrix 6 12 3 3 A. 10 10 C. 30 30 3. 10 7. 3. 30 10 30 152/5 D.…

A: Solution is done in step 2

Q: 3. If a = 2 i-3 j+5k and b = -3 i+6k, determine a simplified vector for each of the following in the…

A:

Q: V. ASSESSMENT (Time Frame: (Learning Activity Sheets for Enrichment, Remediation, or Assessment to…

A: Given

Q: If on V = R² define the usual scalar multiplication « (x, y) = (« x,x y) , and addition (x1, Y1) +…

A: Concept: Vector space: Vector space is defined by the associative and commutative laws of vector…

Q: An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If the oil was…

A: We have to find dR/dt .

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A:

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: (b) 2+ 5y = 2, y(0) = 0 dt

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: describes the position of a particle moving along a coordinate line, where s is in feet and t is in…

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Q: In what instance does the Chain Rule of differentiation applicable? Explain briefly.

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Q: Find the area of the triangle having vertices at (−2,3,1),(1,2,3) and (3,−1,2)

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Q: 3. Evaluate: lim x-0 (sinx

A: According to Bartleby guidelines we are supposed to do only one question. If you want more to be…

Q: Consider the differential equation r'y" +3ry'-3y 2a - 3r. of variation of parameters to solve the…

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Q: C Fnd the firet order parho derivohve of 4.5 f(x,4,2)= e* +y2 1.

A: We have to find the partial derivatives.   According to our guidelines we can solve only one…

Q: 4. (D2 – 5D + 6)y = 15sinx – 15cosx -

A:

Q: Maximize f(x, y) = xy Constraint: x + 9y = 18 kimum of f(x, y) = at (x, y) =

A: Given

Q: Plot the point that has the given polar coordinates.  2,  3π 4

A: We have to show the given point on the graph.

Q: By considering different paths of approach, show that the function below has no limit as…

A: In this question we have to find the limit.

Q: The area under the graph of f(x) = 3x2 between x = 2 andx = k is 504, where k > 2. Find the value of…

A: Given

Q: Let C(x)= x2+4x+1 dollars be the cost function, where the x represents the quantity. The estimate…

A:

Q: 4 Which formula would be used to calculate the trapezoid approximation of L dx using five…

A: We have to use trapezoidal rule. Option B is correct.

Q: a spherical balloon is filled with gas at a rate of 300 mm3/sec. Find the rate at which the surface…

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Q: The power series representation of 8. f (x) = x +7 centered at x = 2 is: 8 8 8 8 (x-2) + 81 (x-2) 2-…

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Q: x3 + x² + 2x + 1 dx J (x² + 1)(x² + 2)

A: ∫x3+x2+2x+1(x2+1)(x2+2)dxPerform partial fraction decomposition=∫1x2+2+xx2+1dxApply…

Q: 9. Jer'y ds, C:x cos t, y sin 1, z = 1, 0<1s/2 %3D 77

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Q: x° 16x6 -24x3 +9 dx

A:

Q: dx J Vx² – 25

A:

Q: Evauate: |(*+xy) dx+ Cy- xy)dy; C: the x-axis from the origin to 2,0) and then line x-2 from (2,07…

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Q: 2x y= Arccos(e)

A:

Q: On what interval(s) is f(x) increasing? Decreasing? Explain

A: Given the graph of the f'(x)

Q: (in) S 15:22 15-z dx. u = (M S 15 - TV9 – a² dx. u= (vi) S dr. u = 22+15

A:

Q: If the 6th term of an arithmetic sequence is 63 and the 14th term is 135, write the formula for the…

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Q: 4. y = x, y = 2x, and x + y = 6 (Answer: 3 s. u.)

A:

Q: II. Find the Inverse Laplace of the following 2s-9 d. s² +2 1 е. (s²+1)(s²+4s+8)

A: As we know the Laplace transform identity; 1). L-11s2+a2=1asinat 2). L-1ss2+a2=cosat 3).…