. Find the constants a and b such that the function 6, x 5-1 f(x)= ax+b,-13 is continuous on the entire real line.

Q: b) Find the area of the largest rectangle that can be inscribed between the x-axis and the graph…

A: To find the area of the largest rectangle that can be inscribed between the  x-axis and the graph…

Q: (b) L-¹268 32-68+12.

A: Given that :      L-1[(s-3)/(s2-6s+12)]       We find laplace inverse transform.

Q: Find the area bounded by the given curves. y = x² - 13 and y = 2 - 14x² square units Find the area…

A: We have to find the area bounded by the curves.

Q: Evaluate the following integral given f(x) f(x) dx = log 9-8 4 = X X if x < 1, if x ≥ 1.

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Q: x²-100 18. Find the vertical asymptotes (if any) of the function f(x)= x²-16x+60*

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Q: For the following composite function, find an inner function u = g(x) and an outer function y=f(u)…

A: To find out the inner function and outer function and also the derivative of the function with…

Q: Use logarithmic differentiation to find dy/dx. x² - 64 x² + 64 dy dx = y = 1 x8

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Q: Use Gaussian 3x + 2y + 5z = 1 -y +z = 4 6x +49 + 10z = 7 Elimination to solve the set of equations…

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Q: Given x² - y² = 1. dy dt Find dy dt dx dt

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Q: Find the indefinite integral. (Use C for the constant of integration.) e2x 9 + e4x garctan 3 dx +C

A: ∫e2x9+e4xdx Apply u substitution Let  u=e2x &amp; dudx=2e2x ⇒du=e2x2dx…

Q: 5 If sin(x) = - and is in quadrant I, determine the exact value of each of the following. Use 8…

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Q: The graph of f'(x) is shown below. The graph of f '(x) NOT f(x) Area - 12 (b) Area = 16 a) [5 F²(x)…

A: according to bartleby guideline we do only first three parts of multiple questions. graph of f'(x)…

Q: Find the volume V of the described Solid S. The base of S is a Circular disk with radius r. Parallel…

A:

Q: Suppose that a particle moves along a straight line with acceleration defined by a(t) = t – 5/2 in…

A:

Q: a. Write the equation of the line that represents the linear approximation to the following function…

A: fx=xx+2,  a=1  &amp;  f1.3 a). Differentiating with respect to x, we get…

Q: Evaluate the integral 0 2πT 1 cos x dx.

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Q: A collector of antique motorcycles is planning to enclose an exhibit in the shape shown below. The…

A: The sides with length x will use a material that costs $5 per foot while the sides with length y…

Q: Find the limit: lim x → 169 X X 13 169 Give your answer to at least three decimal places:

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Q: 2x cm b) Show that the volume of the cuboid, V, is given by 675x² 2 Figure 2 Figure 2 shows a cuboid…

A: The volume of a cuboid with length l, width w and height h is given by V=l×w×h

Q: Use implicit differentiation to find y² + 3x³ dy dx = = 4y - 2x² dy dx

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Q: Use trigonometric identities and algebraic methods, as necessary, to solve the following…

A: 4cos2(x)+4=6

Q: 2. The acceleration e²t - 25 of a particle at time t > 0 is given by a(t) + 2. Given that the…

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Q: Find the slope of the tangent line to the curve - 5y³ + 5x²y² = 10 at the point (1, − 1)

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Q: 1. -6 -5 The graphs or the polar curves r = 3 and r = 3+2 sine are shown. -4 R -2 -1 0 -2 = 4 6 Part…

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Q: Find the ane between the planes x-2y-3z=2 and 3x-y-2z=4 a) 142 degrees b) 94 degrees c) 38…

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Q: An airplane is flying horizontally away from an observer at a rate of 300 meters per second. The…

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Q: find the radius of convergence of the series x^n/n+1

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Q: Using the graph of the function H(x) below, find the following. 10+ -10 -10+ 5 Š SH(x) dx = -7.6…

A: By using the graph of the function Hx, below to find the following. To evaluate ∫-7.65Hx dx.

Q: Find the area of the region bounded by: r = 9 - 2 sin

A: Area bounded in the polar region is given by A = 12∫r2dθGiven expressionr = 9 - 2sinθ

Q: Find the limit a) lim (x³ + 4 sin x) X--0 c) lim sex-s X->>0 S+sex b) lim (3 cos x + 3 sin x) x →/…

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: Q9 Determine which function has an absolute maximum. (a) f(x) = x³ + 2x - 1 (c) f(x) = x² - 2x + 7…

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Q: ← dy Find for the following function. dx dy dx 5 cos x y=8-9 cos x 11 40 sin(x) (8-9 cos(x))²

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Q: 5. f(x,y) = (x²y+ 3x) 5 A. fy B. fyy (1,-1)

A: To find out the partial derivatives.

Q: f(x) = 6x from a = 1 to b=2 (a) Calculate the Riemann sum for the function for the following values…

A: To find the area of given function.

Q: 1² 2t 1+1² 1+1² A submarine is traveling such that its position vector s(t)=, where s is in miles…

A: A submarine is traveling such that its position vector st=t21+t2, 2t1+t2, where  s is in miles and t…

Q: The demand and supply functions for Penn State women's volleyball jerseys are: P = d(x)=x²-3x + 132…

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Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Green's…

A: C is the positively oriented square with vertices (0,0),(3,0),(3,3), and (0,3). Line Integral…

Q: f(x) = √√/23 — x. Express with interval notation, using U for the union of sets and inf for ∞.…

A: f(x) is given, we have to find Domain and range of this function.

Q: Consider the function f(x) Let F(x) be the antiderivative Then F(2) = 5 4 x4 x6 of f(x) with F(1) =

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Q: Evaluate [₁x (x + y)ds where C is the straight-line segment x = t, y = (2-t), z = 0 from (0,2,0) to…

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Q: If ƒ(x) ƒ'(x) = - 53 x - 7' what's f'(x)?

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Q: der (volume V = r²h) has a constant volume of 100 cubic feet. If its height is second while the…

A: Topic:- application of the derivative  as we know that volume of the cylinder is  volume V = π r2h…

Q: Q12 Find and classify all critical points of f(x) = x³ - 3x² - 4 using the second derivative test.

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Q: The projected rate of increase in enrollment at a new college is estimated by dE/dt=6,000(t+4)^-3/2…

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Q: 3 Use the definition of the definite integral to evaluate (5x+1) dx. Use right Riemann sums and…

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Q: Find the arc length of the curve below on the given interval. 3 5/3 3 1/3 y=5* 4x +5 on [1,27] -X…

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Q: is the set of all real number except f(x) = x +4 x + 2 and its range is the set of all numbers…

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Q: 2. Find an equation (parametric and vector form) of the line if the line is perpendicular to the…

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Q: 7. Express the Cartesian coordinates in polar coordinates in two different ways. (2,0) b. (-1, √3)…

A: Express the cartesian coordinates in polar coordinates in two different ways a) (2, 0)  b)…

Q: 6. Convert the polar coordinates to Cartesian coordinates. (4, 5) b. (-2,5) a.

A: (a) given polar coordinates, (r,θ)=(4,π6)