Question Find the value(s) of k that makes the given function continuous. 3 if x < k f(x) = { = { ²³x+4 ifk ≤x≤5 (Use a comma to separate multiple answers. Enter an exact value or values.) Provide your answer below: k =

Q: lim h0 lim 3 X x²) x + h) - h √x+h=√x

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Q: (A) If y = 5x x² - 4 dy dx dy dx dy dx dy then = dx −5x2 — 20 (x² - 4)² 5x2 – 20 (x²-4)² −5x2 +20…

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Q: Find (f. f)(x). X 8x + 49 Find the domain of (f. f)(x). (Enter your answer using interval notation.)…

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Q: 4- x x-45-√√x² + 9, lim X→4 9-x² x-35-√√x² + 16, lim

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Q: Given the vector function 7 (t) = (cos 2t, sin 2t, t), find 7(2), Ñ(1), B(4)

A: Given that  r→(t)=cos2t,sin2t,t

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A: According to bartleby guidelines,  we are supposed to do only one question  with 3 subparts.  If you…

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Q: Given f(x) = find f'(4) using the definition of a derivative. x-1 Provide your answer below: f'(4) =

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Q: Evaluate √ ²2x² -8 ²³√x² dx indefinite integral

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Q: 1. For the function y = 5x³ - 4x a. Determine the average rate of change between x₁= 3 and x₂ = 5.…

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Q: The slope of the tangent line to f(x) = cos(x) sin(x) at x = ㅠ 2 5

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Q: 118. [T] y = 3x² + 4x+1 at (0, 1)

A: Topic = Functions As per guidelines , At a time only one question can be answered. please repost for…

Q: 2. Find the general solution. a) a' = -(2/t)x+t. b) y'+y=e². c) x² + 2tx=e-t² 1. First-Order…

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Q: Find the area of the shaded region. 72 e-1 على E -1.0 -0.5 14 12 10 y= 5e/ 8 0.5 (1, 5e) y=5xex² 1.0…

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Q: Question 28 Find the equation of the curve whose y" O y = 2 sin ¹(x). y = Question 29 y=sin-¹(x) -…

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A: Given Graph:-

Q: Use the equation f ′(a) = lim x→a  f(x) − f(a) x − ato find f ′(a) at the given number a. f(x) =  x2…

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Q: Evaluate the integral. 56 So ex Jo 8x² + 9x + 1 1 dx

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Q: Find the slope of the tangent line to the curve f(x) A 63/16 -63/16 C-16/63 D 16/6 1 3x³ + 2x² - 4x…

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Q: 4. 5. cy² = x² + y x = A sin(wt + ß); w a parameter, not to be eliminated

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Q: Let f(x) = 1 x-2 Find and simplify the difference quotient: f(x)-f(a) x-a

A: Given that:  f(x) = 1/(x-2) . And we find. ( f(x)-f(a))/(x-a).   We know that l.c.m.of : 1/x +1/a =…

Q: Find parametric equations for line that is tangent to the curve x = (cos(3), sin(-3), 3).…

A: If a curve given as r(t)=x(t),y(t),z(t) then parametric equation of tangent line at a point…

Q: Find the local minimum of the function f(x), which is given in the graph below. -8 Provide your…

A: Solution

Q: choose the correct answer The grades of Michelle in seven subjects are 84, 91, 94, 84, 92, 91, 93…

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Q: Find the area of the shaded region. 75 15 15) -30 x = y² -10 y -20 x=5y-y -10 -5 -10 X

A: To find the area of the shaded region.

Q: For the given function find the average rate of change over each specified interval. f(x) = x2 + x −…

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Q: B/ Represent the plane (2, 4, -6), the top line locates in this plane, the point B(1, ?, 2) locates…

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Q: Length of a Curve Find the length, L, of the curve given below. L-0 y = -√ √6¹-1dt, 3≤x≤6

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Q: A tank of cylindrical shape originally contains 180 liters of water and has 5 grams of salt (the…

A: This is a linear differential equation problem. see below the answer and calculation

Q: Given f(t) = sin² t + cos² t g (t) = sec² t - tan² t evaluate f(T) + g(n) B

A: Solve the following

Q: choose the correct answer Which recursive rule best describes the sequence  -3, -1, 5, 23, 77 … ?…

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Q: 3. Find the plane that satisfies the following conditions: (a) The plane that passes through the…

A: As per the guidelines I am supposed to do the first question among multiple questions. To get the…

Q: A math tutor makes $15.00 an hour. An additional $7.50 is added if she works past her normal 40 hour…

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Q: .Consider the hemi-spherical tank of radius 13 m as shown in the figure (not drawn to ale). What is…

A: Topic = Volume

Q: Finding the Average Value of a Function 51. f(x) = 9x², [-3,3]

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Q: 1. Solve d²y 1 1 1²2-69² +9y = 6³² (√2-²2²-27) dy 6. dx² dx

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Q: 1) lim x² - 16 x 4 x + 4

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Q: Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an…

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Q: Find the arc length of the curve r* (t) = (cos³ (t), 0, sin³ (t)) from t = 0 to t = FIN ㅠ

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Q: Projectile Motion The range R of a projectile is vz R= (sin 20) 32 where vo is the initial velocity…

A: Need to find out the change in the range.

Q: Solve the initial-value problem. xy'−y=xlnx, y(1) = 5 O a. y(x) = 5x(In x)2 O b. C. y(x) = 5xln x +…

A: The given equation is; xy'-y=xlnx, y(1)=5.

Q: Consider the function g(x) = a sin²(x)+1 kx+1 2x+1 if x T 2

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Q: For x ≥ 0, find functions f,g,h so that fogoh (x) = (2√ Oh(x)=x4, f(x) = 2x+x², g(x)=√x g(x)=x4,…

A: Topic:- function

Q: 5. Give a rough sketch of the quadric surface y = −x² − z² + 5.

A: since the given surface is 3d so it need to be plot on 2d on paper by assuming z=1

Q: Let f(x) = −sin(x)and g(x) = cos(x). Find [f(x) g(x)]. dx d -[ƒ(x) • g(x)] = sin²(x) - cos²(x) dx d…

A: This question can be solved using product rule of differentiation.

Q: H Question Completion Status: QUESTION 4 State the domain of: g(x) = □ (-∞, -2) U (-2, ∞ ) O(-∞,2) U…

A: We have given function  gx=x+3x2+x-6 Domain is the values of x for which a function is defined.…

Q: Identify the parent function of f(x)=-4 |z-2.

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