if x<1 f(x) = %3D 2x – 1 if x 2 1 if x > 1

Q: * 36sin(t)dt Evaluate the limit lim

A: we will use differentation rules to find the limit

Q: MATH241 Linear Algebra and Ordinary D...

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Q: Show that the line joining the points A (2,3,-1) and B(3,5,-3) ,C(1,2,3) and D(3,5,7)

A: Explanation of the solution is given below...

Q: Let C be a real number and let f(x) = 6C. If the slope of the tangent 3 line to the graph of f(x) at...

A: Finding 1st and 2nd derivative to solve the problem.

Q: The region bounded by the graph of , x-axis, and the line x=2 on the right is rotated about the line...

A: You haven't mentioned the function. Kindly upload the same with complete details. 

Q: If f(x) = 2x? (a, b) is y = -4 and the equation of thenormal line to the curve at the point ax + c f...

A: The given curve is  f(x) = 2x2 - ax - 4..... (1) Equation of normal line on the given curve at (a, b...

Q: 8) Find the equation of the line that passes through the point (-7,9) and perpendicular to the line ...

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Q: Se-*sin 4x dx

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Q: Suppose that ∑ an and ∑ bn are series with positive terms. Prove that if         and ∑bn converges, ...

A: Consider the given limit, limn→∞anbn=0 by the definition of the limit we know that there exists an N...

Q: 4 - Which of the following is the shortest distance from the point (5, 0) to the curve y = V2x ? 7 b...

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Q: Find the particular solution of the following differential equations.

A: 3) Given differential equation, 5v-udu+3v-7udv=0

Q: Solve the following inequalities and show their solution sets on the real line 6/ (x - 1) ≥ 5

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Q: (differential equation question) Determine general solution of the differential equation

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Q: differentiate the following functions

A: We will answer the first question since exact one wasn't specified. Please resubmit the question spe...

Q: Find the integration: x sin(2x) dx

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Q: Find an equation of the tangent plane to the surface z = √(x2 + y2), at the given point (3, 4, 5).

A: We have given equation z=x2+y2 First we rearrange the equation of the surface into the form fx,y,z=0...

Q: Evaluate the limit lim S* 24sin(t³ )dt 26

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Q: Let a be a constant. Given that -104 3a* In(az)dz = e5 ( 40 - find In a. Türkçe: a sabit bir sayı ol...

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Q: find the derivative of y with respect to the appropriatevariable. y = cosh-1 (sec x), 0 &lt; x &lt; ...

A: Consider the given hyperbolic function, y=cosh-1secx use the chain rule of the differentiation which...

Q: differentiate  the following hyperbolic function,,

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Q: Find the intervals on which f(x) =x2-3x+8 is increasing or decreasing

A: Solution: The objective is to find the intervals on which f(x) =x2-3x+8 is increasing or decreasing

Q: Solve: (x - 1)2 = 5.

A: Given equation: x-12=5 Recall the formula a-b2=a2-2ab+b2 Apply the formula in the above equation, we...

Q: Let a be a constant. Evaluate ((x* + a? + a) sin(10r) + 9a)dr.

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Q: Using the Formal Definitions

A: A constant function is the function for which we can put any input value we always get the same cons...

Q: Use the given graph or the table to determine a solution of the given equation 2x3 + 11x2 - 7x - 6 =...

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Q: Find the vertices and locate the foci of the hyperbola with the given equation y2/4 - x2/1 = 1. Then...

A: Given that: The equation of the hyperbola is y24 -x21 = 1 .

Q: Let a be a constant. Given that -107 3x In(ax)dx = el8 ( 42 – 3. find In a. 3 %3D

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Q: Let a be a constant. Evaluate 2 ((2* + 2² + a) sin(4x³) + 12a²)dx.

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Q: 1) Bir f(x) = (x² – 3x + 2)² | domain of function, axes cutting points, asymptotes if any, local ext...

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Q: 6. Solve each inequality by first completing factoring the left side and creating a sign chart. x² +...

A: Given that x2+3x-10x2-6x+9&lt;0 Solve the given inequality by writing interms of factors      

Q: Find the area of the region lying between the x- In(9x) – 1 axis and the curve y = to the right x2 o...

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Q: Evaluate [4/5+91 +12(5+91)' dt .

A: Given,        ∫45+9t+125+9t7dt

Q: Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval ...

A: Given data: Mean value of function is m=4. And ∫258fx+Kdx=34.

Q: Define Orthogonal Trajectories ?

A:         Definition of Orthogonal trajectories:        Given a family of curves , an orthogonal traje...

Q: х у -=1 meets the x-axis at P.Find the a b X The line - equation of the line perpendicular to this l...

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Q: Calculate the limit, if any. a) limx⟶0   x                         1 - ex b) limx⟶4  x2 − x − 12    ...

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Q: Let a be a constant. Evaluate .2 ((x* '+x² + a) sin(9æ³)+ 9x?)dæ. Türkçe: a sabit bir sayı olsun. .2...

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Q: Define the term One-to-One Functions?

A: Definition of One-to-One functions:

Q: Let a be a constant. Given that * (24-) 62 find In a 3. 3z In(ar)dr = e° ( 24 3.

A: We have to use integration by parts first.

Q: 4x + 5 6 - Evaluate the integral dx. V3 – a? a)5 arcsin V3x + 4/3 – a2 + C b)5 arcsin V3x – 4/3 – x2...

A: =?  

Q: Centers of mass for general objects Consider the following two- and three-dimensional regions with v...

A:   The center of mass wit length s and base b is:                                            

Q: Which of the following is FALSE for the graph of the function f(x) = xe"? %3D a) fis increasing and ...

A: The given function is, fx=xex

Q: If y = (1 + x) then what is the value of y'(0)? a) 0 b)-1 c) 1 d) -2 e) 2

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Q: Suppose that a continuous function g satisfies: | 9(x)dx = 36 and | 9(2z)dx = 15. 2 | eg(3z)dr. Find

A: We have to convert all functions to g(x) using integration properties.

Q: If sine + cos0 =p sec0+ csc0 =q Then show that q(p² -1) = 2p

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Q: I have to identify at least five conversion factors

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Q: 1- Determine. 4. Cos 'x sinX dx

A: Given:                     ∫cos4(x) sin(x) dx     Solution:                    Integrating the given...

Q: Can you solve this question step by step?

A: Given that (A) sin x1+ydydx=cos x Separating the variables, we get 11+ydy=cos xsin xdx11+ydy=cot x d...

Q: Which of the following is the shortest distance from the point (5, 0) to the curve y = /2x 5 a) 2 b)...

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Q: Use Leibniz’s Rule to find the derivatives of the functions

A:   Use Leibniz’s Rule to find the derivatives of the functions