f(x) = x? — 4х

Q: Q5. Use variation of parameters to solve the nonhomogeneous ODE. y" + 16y = sec³4x

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Q: Evaluate lim dx d cva sin ť dt . t x→0+

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Q: 3. EVALUATE AS AN INFINITE SEMES: 0.5 a. e dx lim x- In (1 + x) b.

A: We know that, ex=1+x1!+x22!+x33!+x44!+.........................=∑n=0∞xnn! and…

Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x 4 A) 을 B) 0 530 C) D) Does not exist

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Q: Find lim eR dt x 00 1/e 1 e

A: We will find first integration then after we apply limit

Q: Let f(x, y) = sin(3x + 5y) and P = 3 Find the maximum rate of change of the fucntion f at the point…

A: Find gradient of f(x,y). Find compute the point . Take the magnitude of the same .

Q: Find lim (e* +x3/2+2x)/x. x+0+ e3/2 а. +00 Ob. Oc 1 d. e9/2 е.

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Q: Find dy/dx of the following function using Chain Rule. y=(x3 + 3)5

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Q: Solve dx dy for y= sec (In x) In (tan x)

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Q: lim 4 sin(x + n) + 3

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Q: Find the line tangent to the graph of f(x) = cos(x) at xo = T.

A: f(x)= cos(x)  Then, f(π) = cosπ⇒f(π) =-1

Q: O Find lim (X,Y)→ LD,0) **+3y* or show it DNE.

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Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

Q: use the chain rule to find dy/dx for the followingy=tan(2x-x^3)

A: Formula used:

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: Use the limit definition of the derivative function to find 4 x2]. dz Which of the following sets up…

A: The objective is to use the definition of limit to find the derivative.

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: Evaluate , x? dx by limit definition. f(x) dx f(G.) Ax¡ lim i=1

A: Given integral  ∫01x2dx △x=b-an△x=1-0n=1n ci=a+i(△x)ci=0+i1nci= inf(ci)=in2

Q: Find dy/dx for f(x)=(Inx)x^2

A: Given:y=fx=lnxx2We need to find: dydx

Q: 1 -1 lím (x,y)→(0,0) tan x² + y?

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Q: Find the limit (2x + y)² lim (x,y)→(0,0) 4x² + v² (Enter dne if the limit does not exist)

A: WE CAN FIND LIMIT . So , we can find limit along the line y=mx .i.e, we can choose path.If for every…

Q: Determine the 2.x2 – 4x + 6 dx using the definition. (hint: lim Rn)

A: Given: ∫12 2x2-4x+6 dx  To find: Value of the limit.

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: Evaluate: limt o sin 3t t5 (t-1)² using L'Hôpital's

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Pls help ASAP

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Q: For f(x)=√7x+2, find f′(x) using the definition f′(x)=limh→0f(x+h)−f(x)/h. f′(x)= Using this, find…

A: Equation of the line passing through the points x1,y1 and having slope m is y-y1 =mx-x1.

Q: OF# Usc the L'Hospital's Rule to compute the limits: B) lim x+5 B00 2x+5* A) lim log, (1+ 2x+x?) and…

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Q: 1. Use the delta method, 2 BONUS MARKS y = 5x² dy dx = lim h-0 f(x+h)-f(x) h to find dx for the…

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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: Find the limit of the function along the x-axis xy lim (x.y)-(0,0) x2 + y?

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Q: Find the limits by rewriting the fractions first.

A: We have to find the limit: limx, y→0, 01-cosxyxy Rewriting the fraction using trigonometric formula,…

Q: dy Use the formula dx Ay lim f (x + Ax) – f(x) lim - Ax→0 Ax Ax dy when y = dx 1 to find x + 5 dy dx

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Q: Q7) If y = tant ,x = tan't at t =- Find by using Chain Rule

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Q: Q3: Find lim,- (2 – sin –) إجابتك :Q4 For (3x³ – 5x) V2x+1 find dy/dx at x=0 إجابتك

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

Q: 14x(e^(1/x))−14x limit x approaches infinity using lhospitals rule

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Q: Q2: Evaluate: 2 In cosy, [1] limy-o [; y4

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x²yeY (x, y) → (0, 0) x4…

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Q: Q2 \ Evaluate .1 dx by using trapezoidal rule. 1+x2

A: See the details solution in below

Q: Evaluate the limit *dx – x – 4aª lim 3 A) В) 1 C) D) 4 E)

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Q: Evaluate the limid lim X'sin t X→o sin x?

A: We have to find limit

Q: Explain the difference between t dx dx lim + lim s-0+ dx lim dx +

A: ..

Q: Find the limit: lim (1,y) → (0,0) x² + 8y?

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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: Find for the following function: dx 4- y = In2 5- tan-1 V4x - 5

A: Topic : differentiation

Q: compute dy/dx using the limit definition. y = 4 − x2

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Q: Find dy/dx of the following function using Chain Rule. y=(-3x5 +1)3

A: we use chain rule for differentiation y=(-3x5 +1)3 dy/dx =3(-3x5 +1)2(-15x4) dy/dx = -45x4(-3x5 +1)2…