II. Directions: Find the slope of the line tangent to the given curve at the indicated point 10-12. f(x) = 9+ 8x - 2x² at (-1,-1) 13-15. f(x) = x=1 at (2,3)

Q: A) Suppose that f(5)=-8, g(5)= 2, f^’(5)=10 and g^’(5)=-4, find h^’(5)=, if h(x)=[f(x)+2g(x)]^4 B)…

A: Suppose that f(5)=-8, g(5)=2, f'(5)=10, g'(5)=-4

Q: A population grows according to the model, 1400 e 0.06t where A is the population t years after the…

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Q: The amount of a certain substance in a chemical compound is given by the function C (t) = 20.6…

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Q: 2. (4x³ - 3x² + 2x) dx

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Q: ular bird sanctuary with one side along a straight river is to be constructed so that it contains 72…

A: Please refer to the image below

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A: Given: Now,     v(t)=f'(t)      =-16t2+286t+10'       =-32t+286

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Q: Solve the DE using laplace transformation: y''(t)-y(t)=4cos(t); y(0)=0, y'(0)=1 the answer should…

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Q: 2. A cyclist applies a force F with magnitude F = 50N in the same direction as the vector b = 4 j.…

A: We have to find the vectors.

Q: I f 1 1-y Evaluate O a. 16 946 O b. 16 936 O c. 8 945 O d. None of the choices. O e. 16 945 xy₁√//1-…

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Q: Given Cost and Price (demand) functions C(q) = 100q+40000 and p(q) = -2.8q +800, what profit can be…

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Q: Give the Taylor series of the function f(x) == 1 3x²

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Q: 3. Use the cross product properties to prove the relation (a - b) × (â+b) = 2(â × b) given a = (1,…

A: Given,a=i-3j+2kb=-2i+0j+k

Q: Evaluate the following integrals. Show the solution. 1. fcsc² (7x + 5) dx 2. x² sec (4x³ +9) dx dx…

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Q: 3.lim X→π In(cos2x) (π - x)²

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Q: Find the present value of $10,000 due in 8 years if the interest is 4.8% compounded continuously. O…

A: topic- exponential function

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Q: x = 1. 2. Find the derivative of f(x) = 3x² - 5x at x = 1 using the formula f'(x) = lim f(x)-f(xo)…

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Q: consider the function y=−3sin(4x−π/2)+1  a) What is the amplitude? b) What is the period?  c)…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Given

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: 1. Find the Inverse Laplace Transforms of the following. 4 1) -1 S-3

A: The general formula we have that  Laplace transform of eat u(t) is 1/(s-a)

Q: 2) dy = y² (1+ex) dx

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Q: The given definite integral is equal to x3 dx Jo x + 1 O 1.23 O 0.43 O 0.18 O 1.42 Onone of the…

A: The given integral:∫01x3x+1We need to evaluate the definite integral.

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: 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: Find in the parametric equation d'y dx² x = 5 sin² t y = 2 cost 0≤t≤ 2π.

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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: Evaluate the integral √ (k+ 2) ( k + 3) dx

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: tanx - x x-0 x - sinx 1. lim

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Q: A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its…

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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: IVICCE dy Find from the following equations dx Problem (iii) x³ + xy = 0

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Q: The equation y-(5)=2(x-(3)) in slope intercept form is y=?

A: The equation y-(5)=2(x-(3)) in slope intercept form is y=?

Q: 100 (e) Σ199 2i(i3 – 1) i=1

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Q: Use double integration to find the volume of the solid on the first octant enclosed by the curves x²…

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Q: Find the equation of the family of curves having the given slope, and the equation of the curve of…

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Q: You deposit $2000 in an account with 4% annual compound interest. Complete the following, assuming…

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Q: cos 3t dt 5 + 3 sin 3t Ocos 3t

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Q: 4. [7.4 & 7.5] If... a = i +3j - 2k, and b=i-3j-k, and c=2i+j-k, then... a) Determine (ā- 2b) b)…

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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: Classify the following ODE's with respect to order and linearity. a. 3x-y' - 5y = 7x³ - 8x+1

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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: Given f(x,y) = 6x^2 - 2x^3 + 3y^2 + 6xy. Determine any local maxima, local minima, and saddle…

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Q: Evaluate efffxv xdv,where D is the tetrahedron with vertices (0,0,0), (2,0,0), (0,2,0) and (0,0,2).

A: Given problem:- Evaluate  ∫∫∫D xdv ,where D is the tetrahedron with vertices (0,0,0), (2,0,0),…

Q: 21,n *** a1,1 1,2 1,3 02.n ... 0 02,2 02.3 0 0 03,3 03.1 ... 1 0 00 Onn, field K and n € Z₂1.…

A: The matrix,M:=a11a12a13..a1n0a22a23..a2n00a33..a3n............00000ann∈Matn×nK be an upper…

Q: Find the linearization f(x) = √x, L(x) = L(x) of the function at a. a=4

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Q: 1. Given the following vectors: u=(1, 2,-4) and v=(2, 3, 5) Find: a) u.v b) u.u c) (u.v) v d) angle…

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Q: 1 - ₁ - £x² = 1 + x + x² + X x=0 +++1-23-²² 3! sin x-(-1). cos x=(-1)- -(-1*- 1 - 2 + 1 - 4 - =…

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Q: Calculus Use the Table of Integrals to evaluate the integral. 1₁ 21²6 2t²e-t dt

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…