If f is continuous on [0, 0) and f(x) dx diverges, then lim f(x) + 0.

Q: compute f ' (a) using the limit definition and find an equation of the tangent line to the graph of…

A: Plug x=4 to find f'(4) Answer: f'(a)= -1/16

Q: Q3) Using the definition, lim f(k+h)+f(k) h-0 ds calculate the derivatives dk h of the function : k…

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Q: Use the limit definition of the derivative function to find 4 x*]. dz Which of the following sets up…

A: We need to evaluate an equivalent expression of the following derivative using limit definition…

Q: (a) Find the exact value of the overshoot lim E 1/1- dx/x?

A: Given limn→∞∑j=1n1/j2-∫1πdxx2

Q: For the function given by q (x)= x² + 2x+1, use the limit definition of the derivative to compute…

A: Definition of the Derivative:        The derivative of f(x)  with respect to x is the function f'(x)…

Q: Find the value of the limit below. [4 – 6(x + Ax)]? – (4 – 6x)² - lim Ax → 0 Дх Specify the function…

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Q: Choose the correct answer for the following limit S sin t3 dt lim 3x4 (A) (8) -1 (C) 1 4 (D) 4. (E)…

A: Let us consider the function F(x)=∫a(x)b(x) g(t) dt Then the derivative of the function is given by…

Q: I. Evaluate the following limits. x sinh x 1. lim x-40 cos 3x – 1

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Q: et+ e-X-x2-2 d. lim- x→0 sin²x-x

A: Since there is the symbol of limit, hence limit of the function helps to find the answer to the…

Q: Based on the given values, is the function continuous or not? If not, select the condition which is…

A: In the given question we have to tell such function which satisfies the given three property and and…

Q: Evaluate the following limit. sin xy + cos xy 2y lim (x,y) →(0,)

A: The objective is to evaluate the limit.

Q: Find the limit. t2 j+ sin(7t) k sin2(t) -2t ¡ + lim t→0 e

A: We have to find the limit: limt→0e-2t i+t2sin2t j+sin(7t) k

Q: > If f is a continuous, decreasing function over [1,0) and the lim f (x)=0, X00 then :)dx is…

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Q: C- The result of the following limit is lim 1-0 sin t² t f

A: limt→0sin t2t

Q: Choose the correct answer for the following limit So sin t3 dt lim 2 x4 (A) 1 Q1_V1_M (B) (C) 1 8…

A: Given:

Q: Choose the correct answer for the following limit Q1_V1_M S sin t3 dt lim x-0 1 2 x4 (A) 3. (B) -1 3…

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Q: What is the limit of (e^x-e^-x)/( sin (x)) as x approaches 0?

A: we have find the value of limx→0ex-e-xsin x

Q: To apply the divergence test for ,3/n² n=1 we need to evaluate lim e3ln? n→∞ What is the value of…

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Q: Computing the derivative of ƒ(x) = x2 ex

A: Consider the given function fx=x2ex

Q: lim; 0 (, cos t, In t). t+1

A: limt→01t+1, cost, lnt

Q: Find the limit as x approaches c of the average rate of change of the following function from c to…

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Q: In each case use the limit definition to compute f'(0), and then find the equation of the tangent…

A: Given: a fx=xex   b fx=x2ex

Q: (-cx² + 2x, (sin x + cos x, x> n x<π 9) Prove that lim (x* sin+5) = 5 10) f(x) = What value must c…

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Q: C-The result of the following limit is sin t² lim 1-0

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Q: Find the limit of the following. V3 sin 0 lim 0→t/3 3

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Q: given f(x) = (2x+1)/(x+3), use the limit definition to find the tangent line to graph of f(x) at x=0

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Q: Q3. Compute the following limits if they exist. 1 (d) lim x sin

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Q: for |x| > 1, 2x2 fx,(x) = 0, %3D otherwise. Let L = lim P(max{X1,..., X,} < n log(v5)). Determine…

A: Let Xn be a sequence of random variables such that,

Q: If ƒ' is continuous on [0, ∞) and lim→∞ f(x) = 0, show that I p'(x) dx = = -f(0)

A: First we will integrate then put limit

Q: Q3) Using the definition, lim f(k+h)+f(k) h→0 ds calculate the derivatives dk of the function : S= k…

A: Using the definition of derivative have to find  dS/dk ,where S( k ) = k + 1/k.

Q: X,xif limF,(t)= F(t) at all t for which Fis Continuous

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The following limit represents the derivative of some function f at sor a. (1+h)" – 1 lim h >0

A: Limit derivative formula is  limh-&gt;0f(a+h)-f(a)h from the given limit we can see that f(x)=1…

Q: verify that L’Hôpital’s Rule applies and evaluate the limit.

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Q: If [ f(x)\dx<∞ show that limf(x)dx=0 k→∞00 1

A: We have to prove that given expression.

Q: 4) If y = (x² + 1)cos(3x), then find dy/dx. 5) Evaluate the following limit e cosx – 1 lim x-n/2 2x…

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Q: The following limit represents the derivative of a functionf at a point a. 5 tan 6. V3 f '(a) = =…

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Q: Evaluate the following limits by constructing their respective table of values. 1- cos(3t) 4. lim 3t…

A: note: as per our company guidelines, we are supposed to answer 3 sub parts of a given question.…

Q: Find the limit using L'Hospital's Rule. e 2x – 1 lim x→0 sin x

A: We use L hospital's Rule

Q: Evaluate the limits of the following functions, and verify your answer. (6x+3y)sin(2x+y) 4x +4xy+ y…

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Q: 70. J, f(x) dx may not equal lim , f(x) dx Show that 2x dx o x² + 1 diverges and hence that 2x dx x²…

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Q: Find the limit of f(x) = as x approaches co and as x approaches - oo. 4 -

A: Given,          fx=-4+2x4-6x

Q: Given. lim e = 2e Use only E- & depini tion of a function limit to Prove: e*+1 dx d e?*** 2a+1 ニ2e…

A: epsilon delta ε-δ - definition of limit Let f(x) be a function defined on an open interval around a…

Q: find the limit as x goes to infinity of ln(x+1/x+2)

A: Evaluate the limit

Q: Choose the correct answer for the following limit S sin t3 dt lim X→0 2 x4 (A) 1

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Q: 1. Show that for all f e L'(R) lim da = 0.

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Q: S, f(x) dr may not equal lim , f(x) dx. Show that 2x dx x* + 1 diverges and hence that 2x dx ? + 1…

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Q: If f' is continuous on [0, ∞) and limx→∞ f (x) = 0 , showthat

A: Given, If f' is continuous on the interval [0,∞) and limx→∞f(x)=0 show that, ∫0∞f'(x)dx=-f(0)

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.