Examples: Find the limits of the following: 1. lim sin x = sin1 = 2 5. lim sec x = lim cos(-) = cos0 =- 『→の

Q: The function given below is discontinuous at x = 1 - 4 I1 O TRUE O FALSE

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Q: 1 Evaluate lim Gnx x→1+ 'Inx х-1

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Q: In R³, consider the triangle formed by X (2,0, 4), Y (0,5, 0) and Z (-2,0,0). Us- ing vector and…

A: Let's find.

Q: 1 у 3 2 y (х + 2)

A: y = (x+2)-1/2 dy/dx = (-1/2)(x+2)(-1/2 - 1) dy/dx = (-1/2)(x+2)(-3/2) dy/dx = -1/2(x+2)3/2

Q: Let F = (5x,9x, 4) and G = (4,9x, 5). Calculate curl(F). (Give your answers using component form or…

A: The given functions are F=(5x,9x2,4) & G=(4,9x,5)

Q: Find f (x) if f'(x) = and f(1) = 25. O f(x)= 16x + 25 O f(x) = 16x +1 O f(x) = 16xl +9 O f(x) = 16x…

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Q: Identify the inside function, u = g(x), and the outside function, y = y = (x2 – 6x + 9)2 u = g(x) y…

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Q: Find u · v, u · u, ||v||². (u - v)v, and u · (3v). u = (3, 12), v = (-2, 3) (a) u. v (b) u.u (c)…

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Q: 7) Determine the particular solution to the differential equation y 3x-2 that passes through the…

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Q: 2. Rewrite the following quadratic function in standard form, identify the vertex: f(x) = 2x + 12x -…

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Q: (1 2. 14 Approximate | * -6) dx using 4 rectangles. It is approximatley : (If necessary, round to…

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Q: r(t) = cos(Tt)i– In(t)j+ vt – 6k; to =7 |

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Q: Give the indefinite integral for the following sum of power functions J(x) = 5x4.5 + 4x3.5 + 4.5x +…

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Q: /3x+10 4 Evaluate lim x- 2- x2- 4x +4 А. 1 В. 3/8 D. -00 E. None of these C.0 B O D E O A

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Q: Consider the function y= >x3 – 9x + 4. a. Sketch the graph of y= x3 – 9x + 4. b. Find and describe…

A: Let's find.

Q: The graph of a piecewise-linear function . for-15xS 4. is shown above. What is the value of (A) (B)…

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Q: From what I know when I was teaching high school students, they tend to use the so called "Two…

A: Let's find.

Q: If the function / is continuous for all real numbers and if f(x)= ² when x*-2, x+2 then f(-2) = O…

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Q: What is the value of the definite integral 61 +2 dt?

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Q: Find the angle 0 (where 0° < 0 < 180°) between the following vectors. Give your answer accurate to…

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Q: 2. For each of the following, state whether the equation is ordinary or partial, linear or…

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Q: y 4 3 2 -6 -5 +4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 y = f\x) -4 1.

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Q: Calculate the work done by the field F when the object moves along the given path from the initial…

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Q: -243 S sx(*)dr J ft]dt =m Find if

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Q: (e) Alternating Series Test: Σ (-1)"-2 3n + 3n

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Q: Si la serie E, a, es condicionalmente convergente, determine cuál de las siguientes series es…

A: The series ∑n=1∞an is conditionally convergent.

Q: 4- x2 Evaluate lim x+2 3- (x2+5)Z 5 3 O NONE OF THESE O 4

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Q: Solve the following system of differential equations. dx —х — у, || dt dy Зх — у dt

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Q: Given the series: k=0 does this series converge or diverge? O diverges converges If the series…

A: The given series is ∑k=0∞-16k. To check convergence of the series we use ratio test. Suppose we have…

Q: x² sinh x dx

A: Let's find.

Q: Give the parametric and symmetric equations of the line that passes through the point (2,6, –1) and…

A: To find equation of line passing through the point 2,6,−1 and perpendicular to both vectors −4,3,−5…

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: Evaluate the definite integral. 7t ej+t O e? - 1 i - elj+ 7 2 O e? - 1 i+ 7 k - O eľ - 1 i - 7 1 k -…

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Q: Use the Product Rule to find the derivative of the function. g(x) = (x2 - 2x + 5)(x³ - 6) g'(x) =

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Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

A: The objective of the question is determine the interval in which given vector-value function is…

Q: Find the general solution of the DE below. Show the method on how you get the roots, not by…

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Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction I|v|| =…

A: The objective is to find the vector v.

Q: Find an equation of the plane through (0, -9, – 1) that is perpendicular to the line x - 2 = 3t, y +…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 7 Ex + 3y +z = 8 Find the normal vector, n,,…

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Q: (a) Estimate the area under the graph of f(x) = 2 + 4x2 from x = -1 to x = 2 using three rectangles…

A: The given function is: f(x)=2+4x2; x=-1 to x=2

Q: Eliminate c from the equatia cxy + c²x + 4 = 0. O x* (y')? + x?yy + 4 = 0

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Q: 4y² – 2² = 1

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Q: 1. Given z, = 5 cos 377 +i sin 37 and z2= 37 +i sin 2 find z,z2 where 0se< 2x. cos 2 2 37 +i sin 2…

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Q: Find the component form and magnitude of the vector v with the given initial and terminal points.…

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Q: Evaluate the line integral fe 3y dx + z? dy + (25 - x) dz over the quarter of the circle of radius 5…

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Q: ind an equation of the plane with the given characteristics. The plane passes through the points (4,…

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Q: Consider the following. u=i+j+k v = 2i +ì-k Find u x v. Determine if uxv is orthogonal to both u and…

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Q: 13 For the sequence an = n +1' its first term is its second term is its third term is its fourth…

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Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). f(x) = 5 sin (4x³) If…

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Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction I|v|| =…

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