For the following function, find the equation of the tangent line at the point (1, 2). f(x)=√9x² - 1 Give your answer in the form y = mx + b.

Q: II. Solve the non-linear equation: 1.) x2 - xy + 2y2 = 16 x-y=2

A: Given:  x2-xy-2y2 = 16        ...(1)x-y =2                         ...(2) To find: The value of x ,…

Q: 1. f³₂ (x² − 3) dx -2

A: Given :∫-23x2-3dx

Q: 2 Find the area bounded by the parabola y = 4x and the line y = 2x - 4.

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Q: Evaluate the integral. (Use C for the const dx 15 √ 5x(1 + 5x)

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Q: 2. -4 1 3 -3

A: to evaluate: -431-3

Q: Q4. Evaluate : O (xy²) dx dy -√1-(x-1)²

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Q: 5. I. Evaluate each determinant. 2 -2 4 L

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Q: Which of the following is an appropriate choice for & when proving the following limit? lim(x² - 2x…

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Q: the Following differential equation ²²=1+ P²

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Q: An 84 cm wire is cut into three pieces. The second piece is 4 cm longer than the first piece and the…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: lim x4 1 x³-64 Ꮳ 5 1 vx2+9

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Q: I. 2.) Simplify. Write "undefined" for expressions that are undefined. 2 5 3 2 41610 + -6 -6 2 2

A: Given:26-64.53-62+1220We need to simplify.

Q: Find the length of the shortest ladder that can extend from a vertical wall, over a fence 2 m high…

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Q: 1 x² + y² = 4

A: Given: 1x2+y2=4

Q: Evaluate csc(π/6)   Enter the exact answer.

A: Solution ) csc(π/6)  Angle in first quadrant  We know that  Sin x = 1/ csc x  x = π/6 Sin (π/6)  =…

Q: The position of an object at time t is given by the parametric equations x = 3t² + 1t y = 3t² + 3…

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Q: p= I.F. = e/P(x) dx Now solve (I.F.) y = f (I.F.) - Q(x) dx 9. Solve the linear ODE using an…

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Q: 3. SET-UP the definite integral that will give the area of the region specified using (a) z as the…

A: topic- area bounded by curves

Q: Let a(t)=20e^-0.3t ( in milligrams) be the amount of drug in a patients body at time t where t is…

A: Given problem:- Let a(t) = 20e-0.3t (in milligrams) be the amount of drug in a patients body at time…

Q: Find the area of the region bounded by the parabola y² = 2x − 2 and the line y = x − 5. 16 17 18 19…

A: y² = 2x -2  y = x -5  Here we have to find intersection point  x = (y² +2)/2  x = y+5  Compare both…

Q: For which value(s) of k, if any, is the function 1 (²) = x [kx² - log₂ (x) 2xk²x + 5 continuous on…

A: Use continuity definition of function

Q: 5. ft² √1-1³ dt 6. J (2x+3) dx (x²+3x-6)⁹

A: We have to evaluate the integrals.

Q: Find the equation of the family of orthogonal trajectories of the system of parabolas y² = 2x + C.

A: Orthogonal trajectory

Q: 1. Find the Inverse Laplace Transforms of the following. 3) 3s³+3s 56

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Q: Evaluate the integral and it gives x x 2 sin+cos sin²x 2 dx 2 In | csc (1/2)x-cot (1/2) x | + 2 csc…

A: The given integral is ∫sinx2+cosx2sin2x2 dx=∫1sinx2+cosx2sin2x2 dx=∫cscx2+cscx2 cotx2…

Q: In the 2000 U.S. Census, a small city had a population of 45,000. By 2010, the population had…

A: Given  Population in 2000 = 45,000  Population in 2010 = 65148

Q: -6 +][]+ 3 5 0 3 -2

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Q: Find the average value of the function on the given interval. f(x)=√x+3; [1, 22] (Type an integer or…

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Q: 6. I. Evaluate each determinant. тут 3-3 4 1 -5 0 -1 -4

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Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

A: Here, the rate of change of revenue after the sale of x calculator: R'(x)=(x+5)ln(x+5)

Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x + 4) in the interval…

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Q: Find the area contained between the two curves y = 3x - x² and y = x + x². 1/3 sq. units 1/4 sq.…

A: Let's find area between two given curves.

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: The height of a ball launched in the air t seconds after it is launched is given by:…

Q: S 1 V1 + v 2

A: We have to find integral

Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: Determine the constants c and d in the equation of the curve y = at (0, -1) and an inflection point…

A: This question can be solved using the concept of functions and derivatives.

Q: Use the chain rule to find, where First the pieces: End result (in terms of just t): dz = dt 江 西 | z…

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Q: Find the linear approximation of the function g(x) = 1 + x at a = 0. g(x) * Use it to approximate…

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Q: The equation P=25sin(2πt)+90P models the blood pressure, P, where tt represents time in seconds.…

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Q: Evaluate SSA, dA, where R is the region bounded by y=x2 and x = y² in the first quadrant. X

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Q: 4. x² + y² = 25 at point (3,4) 2

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Q: 3. [7.3] Determine the dot product between the two vectors below if there are 135° between them as…

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Q: 1. f(x) = 3x + 2, [−2, 2], ƒ (c) = 5 2. f(x) = x² − x + 6,[1,4], ƒ (c) = 10 3. f(x) = 2/2, [-3,-1],…

A: According to the guidelines, we are answering first three subparts. Please repost the remaining.…

Q: 54. Look for the volume of the solid produced by rotating the region enclosed by 1792# T y - x² =…

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Q: 1) If y = (x-a)√2ax-x² + + a is constant. x- -1(*-ª) ,then y' = 2√2ax - x² a² sin-¹ a²

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Q: 6 F 0 28inx Cask ex

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Q: ||. Minor and Cofactor 1. Find the cofactor of 6 in matrix D 9 8 4 2 7 -9 3 4 D = 6 -3 2 3 8 9 3 2 ㅋ

A: Let's find cofactor of 6 in matrix D.

Q: b. SSR ехту dA_ where R = {(x,y) | − x ≤ y ≤X, 0±× 6 2}

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Q: Find the general Solution of the complement of the following differential equation y" - yy) +y =oy=0

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Q: Let f be a twice differentiable function on an open interval (a, b). Which statements regarding the…

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