5. [x² x≤0 x>0 f(x)= Domain: Function: Yes No Continuous: Yes No f(-4)= f(0) = f(3) = -x² +4 Range:

Q: QUESTION 35 Which of the following is the linearization of f(x) = x4 + 3x², if a = -1? L(x) = -10x +…

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Q: 1 اس 3L (A) k=-4, m = = (B) (6) If (ƒ(2x¹)) = 7x³, then ƒ'(x) =: (A) ² (5) 12 3 (B))+ (C) ² 20 (B)4…

A: Note: Since the student has mentioned to solve only question no. (6), so we are solving according to…

Q: Let u = (3,-2) Find the component form and magnitude​ (length) of the vector 6u . The component…

A: Topic = Vectors

Q: A wrench 20 cm long lies along the positive y-axis and grips a bolt at the origin. A force is…

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Q: Find the maximum and minimum values of the function f(x, y, z) = x²y² z² subject to the constraint…

A: Given that , fx,y,z=x2y2z2 and gx,y,z=x2+y2+z2-100 Find the maximum and minimum value.

Q: = The triangle inequality assures us that ||ỷ + w|| ≤ |||| + ||w||. Let v = (2, -3) and find a…

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Q: Find the derivative of y with respect to the appropriate variable. y = (10 – 100) tanh "10

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Q: Use the Midpoint Rule with n Approximation= 2.5 [V -1.5 4 to approximate √x³ +19 dx.

A: The given integral is sqrt(x3+19), x from -1.5 to 2.5 and n=4.

Q: Find the limit lim-0+ xlng10

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Q: Solve the following differential equation (tan(x)-4sin(x)sin(y))dx+4cos(x)cos(y)dy=0 ?=constant

A: The given differential equation is; (tan(x)-4sin(x)sin(y))dx+4cos(x)cos(y)dy=0

Q: Find the slope m of the line passing through the given pair of points. (27, 26) and (20, -16) m =

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Q: 4x² + y² -8x+4y=8 Equation vertices: co-vertices: foci:

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Q: Find the central angle 8. 8 = 2.6667 X rad 0 3 8

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Q: Find the derivative of y with respect to the appropriate variable. y=cosh ¹2√√x+10 O A. B. O C. O D.…

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Q: When a sprinkler is set to full rotation, the water covers a circular section of garden with radius…

A: find the area of the garden that is covered by the sprinkler.

Q: The region bounded by y = e²x, y = 0, x = -2, x = -1 is rotated around the x-axis. Find the volume.…

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Q: Use the substitution formula to evaluate the integral. π/2 S 0 COS X (3+4 sin x)³ 3 O A. O B. O C. O…

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Q: Find the domain and range for each. (a) f(x) = log4 (13x + 8) - 2

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Q: (a) Trapezoidal Rule (b) Midpoint Rule 0.5043435602 (c) Simpson's Rule Te e 0 -3ª²dx, n = 4

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Q: Integrate the following. Reduce answers to its simplest form if possible. (b) Stan* ydy

A: Topic = Integration As per guidelines , at a time only one question can be solved out of different…

Q: 9. Given the piecewise defined function below, determine the value(s) of x such that f(x) = -20.…

A: We need to find values of x.

Q: If f(x) = 4x² 2x + 3, find f'(4). Use this to find the equation of the tangent line to the parabola…

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Q: te the following as a single integral: ► ere b = and c = 13 [ f(2) dz + [ f(z) dz - [ f(x) dx = f(z)…

A: Given query is to write the resultant integral.

Q: roblem #4: For which of the following differential equations is y = 0 a solution? = y² + 2x x(y-7)…

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Q: Find the limit. lim (√²+h-√²) h→0

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Q: M Q1: Find the area of the parallelogram with vertices k(1,2,3), (1, 3, 6), m (3, 8, 6), and n(3,…

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Q: As Claudia walks away from a 264-cm lamppost, the tip of her shadow moves twice as fast as she does.…

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Q: (22) The volume of the solid y=(x-1)(x-3)² about the y-axis is: (A) 4n (B) 2 (23) The arc length for…

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Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

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Q: 8 2/7 4/7 5/9 3/5 x² - 4x +3 x+3x²+x-12° Calculate lim

A: Given that a limit problem and we solve this problem by using L'Hospital's rule. We know that…

Q: 2 8 3) (5x² - 4x) dx = in(cinA) (cose)de

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Q: ind an equation of the sphere that passes through the point (5, 3, -1) and has center (3, 8, 5).

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Q: (v) The vector product a × b. (vi) The direction cosines of a. (vii) The angle between a and b,…

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Q: Obtain the general solution of the following differential equations. 2. (D2-4D + 3)y = 20 cosx

A: Given; The characteristic equation is m2-4m+3=0. So,                  m2-4m+3=0⇒m=--4±-42-4· 1· 32·…

Q: For what value of a is the following function continuous at every x? a²x+2a, x≥2 12, x < 2 f(x) =…

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Q: A rock moves along the parabola x = y² + 2 under the force field F = (x², yeª). Find the work moving…

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Q: A block-and-tackle pulley hoist is suspended in a warehouse by ropes of lengths 2 m and 3 m. The…

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Q: Use careful and correct notation to solve these antiderivative problems. 1. Find the general…

A: Given Function :- fx=6x

Q: Find the derivative y = √x 0 dy dx 7tc 7t cos (t¹0) dt

A: Given problem:- y=∫0x7tcost10dt

Q: What is the rate of change of the function whose graph is a line passing through (3, -10) and (-1,…

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Q: Use graphical approximation methods to find the point(s) of intersection of f(x) and g(x). f(x) =…

A: first of all plot the graph by using any graphical tool (demos)

Q: Find the order 3 Taylor polynomial T3(x) of the given function given. Use exact values. f(x) = (5x +…

A: As we know that taylors polynomial of order three f( x ) = f( a ) + ( x - a )f'( a ) + ( x -a…

Q: 2y (b) y² = = = = y' +t, t y = t² ln t

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Q: Find the limit. lim (4x-√√16x² -5x +9) X-8 O A. B. 88 580 C. 0 2 D. -12

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Q: Sequence 1: Sequence 2: 1, 1, 2, 2 4, 8, 16,... 4 25 8 16 125 625 1. Write out the expression for…

A: Please see the below picture for detailed solution.

Q: Graph the function. y = |x-6+6 O A. 4 -10 Ay 10 -10- 10 Q Q C O B. Q H -10 10 -10- CETTE O C. 10-…

A: Topic = Functions Correct Option = A

Q: The solution to the vector differential equation
 r' (t) = (4e4t , 3t2) given r(0) = (2, -1) is

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Q: 07 Find the binomial expansion of (z-2)^3 *

A: Given,           The expression is z-23.To find : Find the binomial expansion of the given…

Q: K vork Let lim f(x)=17 and lim g(x)= 12. Use the limit rules to find the following limit. X-9 x-9…

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Q: 2. Find the higher order derivative: first, second, third, and fourth derivatives of the given…

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