Evaluate the given imit 1. lim (x-1)? 2 メ→! In x 2. lim 3X - 2 × 3. lim (4x+1) ot x

Q: Determine whether each sequence having the given nth term is monotonic. a. a, = 3+ (-1)"

A: If {an} is an increasing sequence or {an} is a decreasing sequence we call it monotonic If a…

Q: Evaluate the indefinite integral, ſx² sinh x³ dx.

A: To evaluate: I=∫x2sinh x3dx⇒I=∫sinh x3  x2dx

Q: dy given the dx Use implicit differentiation to determine equation x° + y? 10. - dy dx

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Q: Determine the equation of the tangent line to the curve, y = 4x e at x = 1. Use exact values.

A: Given y=e4xx3     at x=1To find equation of tangent:

Q: Find the 2nd derivative with complete solution y = 3x + 5 / x^2 + 4

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Q: An object’s position function, s, in meters, is given by s(t)= -4.9t 2 +13.2t, where t is measured…

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Q: Find the area of the plane region bounded by the given curves: y= x^3, y= x + 6, and 2y+2 = 0

A: Explanation of the answer is as follows

Q: seconds. a) Determine the maximum height and when it is reached, rounded to the nearest tenth. b)…

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Q: 1. In the chart below, you are given a formula. Name the formula. Formula Name of the formula/what…

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Q: Use the properties of limits to help decide whether the limit exists. If the limit exists, find its…

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Q: 4. The derivative of a constant is 5. The derivative of a of two functions is the denominator times…

A: This question is based on Basics of differentiation.

Q: Given the geometric sequence 31, 31/8,31/64 find an explicit formula for an find a7 please show…

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Q: Let C be the cost to produce x batches of widgets, and let Rix) be the revenue in thousands of…

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Q: A factory sells a particular product at a price of (200.01x) in peso per unit. The variable cost per…

A: Concept: Maximum value: To find the maximum value of a function using first and second derivatives,…

Q: Find the center and radius of the sphere. 2 2 5x + 5y + 5z + x +y +z = 16 Center = (OOD. radius = 4…

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Q: Solving bernoulli differential equation -2xy=2xy

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Q: For each natural number n, the expression 2* – 7n - 1 is divisible by

A: Concept: Mathematical induction: Mathematical induction is a mechanism for proving a statement,…

Q: A power representation of the function f(r) = for -1 <a<1 is 1+ %3D

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Q: 1. lim (6x + 1)cotx

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Q: sin x S + 3x)dx 1. cos x dx 8 sin?x cos²x 4. 了 1 2. 了 dx 1-cos x 5. J sec x(sec x – tan x) dx 2 secx…

A: These all are solved by the help of standard trigonometric Antiderivative.

Q: Evaluate the given Integral 1. ſ csc x (cos2 x - 1)dx

A: Solution is done in step 2

Q: +C, vnere B 1s parallel to the vector (1, 2) C is perpendicular

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Q: Question * Let f be a given function. A graphical interpretation of the 3-point central difference…

A: The statement is true. see below the explanation

Q: 12. Find the maximum and minimum values of each function. Graph each function. а. у %3D е* + 2 b. у…

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Q: 8/16/22, 140 PM The Sine & Cosine Laws State whether the given measurements determine zero, one, or…

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Q: Identify the End Behaviors for the function graphed to the right 5+ Right hand end behavior: 3 As x…

A: Given query is to find the end behaviour of the function.

Q: 13. Use a polar integral to find the area of the region defined by - Cos 0 KA<T

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Q: A = (Round to thế heares There is no solution. e the value of a. Select the correct choice below…

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Q: Find the following for the vectors u = 6i + 3j + /2k and v = - 6i – 3j – /2k. a. v•u, Įv], and Ju|…

A: We will solve the problem on vector dot product and projection.

Q: f(x) = 8 cos Tx

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Q: A particle moves along a horizontal line. Its position function is s(t) for tz 0. For each problem,…

A: Given: st=t3-t2-56t We know that  vt=dsdt; at=dvdt

Q: The limit im (x - cn -) lim (x· cos x-00 is an indeterminate form of type 0 · ∞. Select one: True O…

A: Here, the given expression is: limx→∞x cos 1x

Q: Find the slope of the tangent line to the curve - 2x2 + 3xy + 4y° 3 242 at the point (- 1, 4).

A: Solve the following

Q: 4. Find the Linearization of f (x) = sinx at a = 7. Provide your answer as L(x) =?

A: Here we have to find the linearization of f(x)

Q: Write a in the form a = a-T+aNN at the given value of t without finding T and N. 3 (5 e'V5)i+…

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Q: f'(x)=-+e2* +x² and S(1) =. Find f(x) Given %3D

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Q: A seagull, flying above a lake, dives for a fish according to the function h(t)=0.25t -4t +15t ,…

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Q: Given the function f(x) = -x* - 4x determine its critical points and classify them, determine the…

A: We have to find the points and check the nature of function.

Q: al squares fr ame if the pie 16

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Q: To find two real numbers whose difference i and whose product is minimum, we can find minimum value…

A: Topic:- calculus

Q: 6. lim f(x) = +o, lim f(x) = 0 x-1+ x-1- and f(-1) = -1

A: discontinuity

Q: 2y(x? — у + х)dx — (x2 — 2у) dy %3D 0

A: I think mistake in question inplace of -ve sign.

Q: Q2. Do as required 3. Evaluate: lim (-) X0 sinx

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Q: x-1 lim エ→1VX -1

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Q: Refer to the figure below to find the limit lim f(x). X - 00 3.5- 2.5- 1.5- 1- 0.5- 2.

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Q: f'(x)= -+e²* +x°and f (1) = Find f(x) Given 5.

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Q: Find the arc length parameter along the curve from the point where t= 0 by evaluating the integral s…

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Q: dy Find by implicit differentiation dx 4 + 5x = sin(xy*) dy dx II

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Q: Question 1 Determine the inverrse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9)

A: L-11s-a =eat L-1as2+a2=sin(at) and L-1ss2+a2= cos(at).

Q: Find the limit 1-ex lim x+0 10x2 – 18x

A: Here we have to use the concept of limit.