S0, f(t) = le-kt, 0

Q: Find lim f(x). Im f0) -O x-2" X--2" (2.4) (4.3)

A: solution:-left hand limitlimx→2-f(x)=0

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Q: 1. Find the most general antiderivative of the function 12 f(x) = ( 2r + sin(4- r) + 7e

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Q: Find the absolute maximum/minimum value for f(x)=x² – 4x+1 on the interval [(-3, 3] 9.

A: Given: fx=x2-4x+1 and x∈-3,3   The Power law: ddxxn=nxn-1

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Q: The differential equation (x²y-2x- 3)dx+ 2dy=0 O Linear in y Linear in x O Homogenous O Exact

A: Given a differential equation

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Q: is a function of K, and y, and tan - z*e®Y.

A: Given problem:- Z is a function of x and y tan√(y2+x2) =zx e6y  To find:-

Q: [a csc ()- y] do + ædy = 0 CSC O y= x cos(In z) + C O y=D cos (In a + C) O In + cos(E)= C O Ino COS

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Q: 2. A bushfire spreads with burning area according to the following function, A(t) = 160t – 40t2 (in…

A: Let's find.

Q: Let z= y- 4a, a u'v and y-v- 3u. Compute On kum)-(1,1) -

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A: Volume of the box

Q: 1 dv 5 3 v 2 –8v² +24v 2 –32v+16v 2

A: solution:-∫1v52-8v2-24v32-32v+16v12 dvlet v=t2dv=2t dt=∫2tt5-8t4-24t3-32t2+16t…

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A: The detailed solution is given below. Thank you

Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

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Q: f(x) is a functicn given by Icosxl Assume that floe) find the pourier Series for of fe).

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Q: 2. A 15-meter-long ladder is leaning against a wall The bottom of the ladder is pushed horizontally…

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Q: Line m is tangent to the circle. Find the indicated measure. 2. mRST 98

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A: We have to use the u subsitution method

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Q: Use the chain rule to find the derivative of 16 f(2) = 2(– 3x0 – 52)" You do not need to expand out…

A: Given: f(x)=2-3x10-5x916

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A: r(t)=((tan-1(11t))i+tcos(t)j-tkDIfferentiate w.r.t.…

Q: P1: 2 cos-1 x dx 1xo

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Q: Find the work done by the force field F in moving an object from P(-4, 8) to Q(6, 4). F(x,y) = 2* 1…

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Q: d Calculate ri(t) · r2(t)] and d ri(t) x r2(t)] first by differentiating dt' dt the product directly…

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Q: 7. SavT – 1 dr 8. | (x) Væ² – 1 dx 1 dx 5x +1 9. dx 10. 3x + 9 4x – 6 dx (x – 1) (x – 2) 11.

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Q: Q1/ Integrate the following functions 1. ſ csc(5x) dx 2. dx 3. ſ cos (x) dx 4. S sin (x) dx 5.…

A: As per our guidelines we are supposed to answer?️ only 3 question. Kindly repost other question as…

Q: 8. The rationalizing substitutionw + 4 = u² transforms - dw into w+4 A. fu² - 4°du B. 2fu² - 4}du C.…

A: Given: I=∫w2w+4dw  ...1   As we know that; The Power law: ddxxn=nxn-1 And ∫a·fxdx=a·∫fxdx , where a…

Q: The integral of the given function S dx is equal to 4+x2 a. 0.116 b. 0.611 c. 0.117 d. 0.161 e. None…

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Q: Solve the equation xy^3 dx + (y + 1)e^(-x) dy = 0.

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Q: 5. If fvr² - 25 5. If [ Vx? - 25 dx is transformed by trigonometric substitution, then it will be…

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Q: x-1 y = log x+1

A: Topic:- derivatives

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Q: Asec24xdx

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Q: x" Find radius and Σ Va3" 9. convergence and interval for this series n=1 n

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Q: etermine whether f is continuous at c= 0. - 3x if x #0 f(x) 2 x* + 3x %3D if x = 0 f continuous at…

A: Topic:- function

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A: The objective of the question is evaluate area bounded by the given function and use the vertical…

Q: dx (x² + 1)

A: To solve the given integral

Q: is a factor of 2 + 5z2 – 5x +1. - O I+1 O 2z +1 O +2 O 2x -1

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Q: Give your answer correct to Use differential to estimate the value of y 4.01 V4.01 8. four decimal…

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Q: Find the derivative of f(x)= x% (x% + x% +x%

A: Find the derivative

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A: Given, ∫14x2x2-17dx

Q: ady す。e o 25+x2 メp

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Q: Find the general solution of the differential equation dx = xin (xy)

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Q: f (x)= arcsin (x³)+ aretan (4x)

A: derivative

Q: 25. Compute the Riemann sums for the function f (x)=x² on the interval [0,2] associated with the…

A: See this solution in below

Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

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