) In the following exercises, use direct substitution to show that each limit leads to the indeterminate form o/o. Then, evaluate the limit. (a). (b). x²2x-3 lim x-3 x²-9 √x+6-3 lim x-3 x - 3

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Q: Evaluate the definite integral 8 2x² + 7 √x -dx

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Q: Sketch the area bounded by x^2 + 2y = 4 and x + y + 2 = 0 on the image below and determine the…

A: volume of above function is π×175.19 cube unit

Q: If evaluate f f(x) dx = 7 f(x) dx = 8 f2f (x) dr.

A: Topic = Integration

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Q: If f(x) = 1 - log5 x, then f-¹(x) =

A: Given that f(x)=1-log5 x , then our aim is to find the value of f-1 (x)=?

Q: s) Given the piecewise function below, find h(-5) and h(-4). if x < -4 h(x) = { 6x - 7 √x+8 ifx ≥-4…

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Q: If y = 3u² + 2u and u = √² +5, fip S da would be: (6√2²+5+2)(√) (6 (3u² +2u) + 2)(√5) ○(3√2²+5+1)(√)…

A: We can find the derivative as below.

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A: Explained below

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Q: True/False: Answer a) for True, b) for false and mark on the scantron. 24. The following is a…

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A: Here we have to find the value of x.

Q: Evaluate the following limit: lim ²-25 2-5 2-5 O Does not exist. O 0 O-10 undefined

A: This question can be solved using the concept of limits.

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A: Given,            fx=-x2+4x+2            gx=x+2To find : Calculate the area between the given…

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Q: Find the volume of the solid with the given base and cross sections. The base is the circle x² + y²…

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Q: Proor: Let † and g be one-to-one functions. a) Prove that (a) fog is one-to-one b) Prove that (b) (ƒ…

A: We will prove this using the concept of one to on

Q: 2 y²dx + xydy = 0

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Q: r an antiderivative of f(x). Do not enter +cas ver: +c

A: topic:- integration

Q: 5. Use the divergence theorem to evaluate the surface integral ff, F. ds, where S is the sphere x² +…

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Q: For the curve: f(x)=√x-5 the equation of the tangent line when x=9 is Oy--(x+1) Oy--1(x-1) y= Oy- (x…

A: This question can be solved using the concept of tangent and normal.

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Q: The area of a rectangle is given by the function A(x) = 3x³ + 6x² + 4x + 8. If the length is defined…

A:

Q: The base of a solid is the region in the xy-plane between the the lines y = x, y = 4x, x = 1 and x =…

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Q: Given f(x) = 4x+3-2, what is f-¹(x)? Of ¹(x) = log4(x-3)+2 Of-1(x) = log4(x + 3)-2 Of(x) = log4(x-2)…

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Q: 4. Verify if the following equations general solution: are exact and find the 2 9. 2xydx + (1 + x²)…

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Q: 1.0⁰ 7 -2 dy 1+ y² 1 +x³ = π 2x + 3 da is an improper integral 1 - 1 (₂ ² ² ₁ + 2x + 1) dz dx + 1…

A: Given problem:- Which of following  is True? a)  ∫0∞dy1+y2=π b) ∫-2711+x3dx is an improper integral…

Q: This exercise uses the radioactive decay model. The burial cloth of an Egyptian mummy is estimated…

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Q: Consider the region bounded by x=4-y, the y-axis and the x-axis. 1 2 3 4 The volume of the solid…

A: Given:-

Q: x² x² + dx a. -ln2 b. +∞o c. In d. none of the above

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Q: Evaluate

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Q: 7. Solve for cot NI 2 if cos(20) = |L0 5 and P(0) E QIV.

A: Given: cos2θ=-45 To find: cotθ2

Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

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Q: Which of the following equations describes the nth term for the sequence O (3) -1(9)*** 4 1 1 1…

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Q: it is planned to construct a right circular cylindrical steam boiler. the available budget for the…

A: Given data:- The available budget for the cylindrical steam boiler, =1 million=1000000 The cost of…

Q: Consider the following geometric series. 00 = n = 1 (-5)" 9n Find the common ratio. Irl 1 Determine…

A: Given, ∑n=1∞-5n-19n

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Q: If f(x) = 1- log5 , then f-¹(x) =

A: Given that a function f(x)= 1 - log5x and we find f-1(x) .   Here i attached the solution of this…

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Q: •+∞0 4-1² 1 x² + 4x² dx

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Q: The equation for the conic section with focus (x, y) = (c, 0), direc ricity e 1, by choosing c =…

A: Topic:- geometry

Q: Find the equation of the tangent line to the graph of the functic f(x) = 3x² - 4x +5 at the point…

A: Find out the equation of tangent line.

Q: The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.…

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Q: Suppose that h(x) = f(x) g(x) and that we know the following f'(3) = -1, g(3) = 2, & g'(3) = -5.…

A: Topic:- calculus

Q: Determine the directional derivative of f(x, y, z) = xe³+xsinz+x²y at the point (2,0,4) in the…

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Q: Consider points P(-1, 3), Q(1, 5), and R(-2, 8). (a) Determine vector PQ and express it in component…

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Q: What is the equation of a line with slope of 2 and a y-intercept of -6? y = -6x + 2 y = 2x - 6 2x…

A: Concept: The equation of a line is found using the slope-intercept form of a straight line. We need…

Q: The second derivative has already been found and factored to be f"(x) = (5x)(x+2). Use interval…

A: