hat value of the constant c is the function f defined below continuous on (-00,00)? f(1) = Jr² - c if I € (-∞0, 4) cz +4 if ze [4,00)

Q: al bar, whose initial temperature was 30° C, is dropp rst second? (The boiling temperature for water…

A: a) A small metal bar, whose initial temperature was 10° C, is dropped into a large container of…

Q: 6. Consider the three points in the plane and their masses: P₁(5,-1) with m₁ = 4, P₂(-1,4) with m2 =…

A: We have to find the coordinates of the center of mass.

Q: et f(x) x8(x-4)³ (x²+3)8 Use logarithmic differentiation to determine the derivative. ƒ'(x) =

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Q: Find the Maclaurin series of 00 Ε n=0 Τ sin(t) t3 - dt.

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Q: 2. The value of a copy machine is $9565 when it is purchased. After two years its value is $7680.…

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Q: Find the volume of the solid generated when the region in the first quadrant enclosed between the…

A: Region is bounded by y=x and y=x2rotating the region about line x=3

Q: Question: Consider: fex) = x+√√√x a) f'(x) Find f'(x) using the limit clefinition of the derivative…

A: Consider (a) To find  by using limit definition of derivative.(b) To evaluate .(c) To find the…

Q: 4. Find the limits (a) lim x-1 (b) lim x-0 xª+¹(ln x + 1) − x 1-x ((² + 2)1/²) 1/². e

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Q: -5 -4 -3 -1 The above is the graph of the derivative f '(x). How many critical points does the…

A: We  have given graph of f'(x).We have to find the number of critical points for the function f(x).We…

Q: Find the principal needed now to get the given amount, that is, find the present value. To get $600…

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Q: for the second question, could u plz explain in detail why the upper and lower bound change in this…

A: Explain the Doubt.

Q: Write the quadratic function in standard form. f(x) = 2x² - x + 1 f(x) = Sketch its graph. -10…

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Q: ) Define the domain and range of f(x) where f(x) = sin²(x) – 1

A: The function f(x)=sin^2(x)−1 is defined for all real numbers x because the sine function, sin(x), is…

Q: Prove the identity. cosh(x) + sinh(x) = ex cosh(x) + sinh(x) = 2²/²/(₁ x + e -x) + ²/² ( 1 = 2/(1 ||

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Q: 72-75. {Use of Tech} Equations of tangent lines a. Find an equation of the line tangent to the…

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Q: F(x)=3x+(x+10)^2 i just need to know how to do domain and range the (x+10)^2 is supposed to be…

A: given function

Q: The radius of a circular oil spill after t minutes is given by r(t) = √√4t. Find the instantaneous…

A: The Radius of a circle oil spill after t minutes is given by

Q: x² + 1 -2x + A Let f(x)= x < 1 x ≥ 1 (a) Use the definition of continuity to find a value for A so…

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Q: The graphs of the functions f and g are shown in the figure. y -1 Let u(x) = f(x)g(x) and v(x): =…

A: Given: Let  and To Find:

Q: 60 50 40 30 20 10 10 20 30 40 50 60 70 80 90 100 110 120 The daily receipts R( t) in millions of…

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Q: C₁ y = √x - 2 + 1 Show 4 pts, including the endpoint." (No decimals. Is no-calc. formative What are…

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Q: Find a formula for the derivative of the function g(x)=3x2-1 using difference quotients:…

A: g(x)=3x2-1

Q: Let f(x, y) = y²x − yx² + xy. (a) Show that the critical points (x, y) satisfy the equations y(y -…

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Q: Let f(x)= 2x1 3x + 2 a. Find the domain of the function. b. Find the y-intercepts, if any. c. Find…

A: The given function .The aim is to find the vertical and horizontal asymptotes and sketch the graph…

Q: Find implicitly: dx In(xy²z) + x²z² + 2xy³ = 1

A: The given equation is

Q: A hemispherical dome of radius 20 feet is to be given 11 coats of paint, each of which is 1/100 inch…

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Q: Find the derivative of the function below. Use lower case letters. eau a² + b² g'(u) = g(u) =

A: Given,

Q: For the equation given below, evaluate / at the point (-2, 1) (52-y)¹ + 2y³ = 14643.

A: given equation

Q: Describe the x-values at which f is differentiable. (Enter your answer using interval notation.) 3x…

A: To describe the -values at which  is differentiable.

Q: A particle is moving along the x-axis. The position of the particle at time t is given by x(t) = t³…

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Q: A particle is moving along the x-axis. The position of the particle at time t is given by x(t) = t³…

A: Consider the given function as

Q: Find a general solution to the differential equation. 1 1 y" +6y=4 tan 6t - e²t 2t

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Q: Consider the function f(x) = 5x³ — 5x on the interval [−3,3]. Find the average or mean slope of the…

A: Given, f(x)= on interval [-3,3].

Q: Find the indefinite integral and check the result by differentiation. [(5x² + (2x152)dx (3x)² Step 1…

A: To find the indefinite integral and to check the result by differentiation.

Q: Use the method for solving equations of the form =G(ax + by) to solve the following differential…

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Q: lim (x,y) → (π,π/2) cos y - sin(2y) cos x cos y

A: Sin (2a) = 2 sin(a) cos(a) 1/ cos(a) = sec(a)

Q: For the given cost function C(x) = 16900 +500x + x², First, find the average cost function. Use it…

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Q: If the instantaneous rate of change of g(x) at (−1, −3) is 1/2, write the equation of the line…

A: The instantaneous rate of change of a function f(x) at a point (x,y) is the slope of the tangent…

Q: We are given f(x) = 3x2 and f '(x) = 6x. (a) Find the instantaneous rate of change of f(x) at x=4.…

A: Given, f(x)=

Q: 9. An inverted conical water tank with a height of 12 ft and a radius of 6 ft is drained through a…

A: The height of the water tank is h=12 feet and the radius of the tank is r=6 feet.

Q: Consider the function f(x) this interval. = 1 on the interval [2, 11]. Find the average or mean…

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Q: (x² + y² + x) dx + xydy = 0 X = | = 1 Answer: C = 12 Selve using integrating Factor

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Q: Consider f(x) = x² 7 (5+ x)² a) Find f'(x) using the Quotient Rule and the Extended Power Rule. b)…

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Q: Determine whether the equation is exact. If it is, then solve it. e'(7y - 4t)dt +(3+7e¹) dy = 0 A.…

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Q: Find the saddle point(s) of the function:  f(x,y) = 2x3 - 6x + 6xy2

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Q: Find a vector orthogonal to both ⟨1,−4,0⟩ and to ⟨0,−4,2⟩ of the form ⟨1,_____ ,_____ ⟩ 9. Let…

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Q: Show that f(x) = x² + 12x +41 -2 -x² 12x - 31 ifa >-6 2 if x < -6 if x = -6 has a removable…

A: The given function,The aim is to prove the function has a removable discontinuous at  and redefine…

Q: Differentiate the following. y = cos ¹(e²x) b) f(x) = cot-¹(x²)

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Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

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Q: You measure the angle from the ground to the top of the building from a point 95 feet away from the…

A: The figure