Show that the equation сos(x) = e* - 2 has a solution on the interval (0, 1). Justify your answer. (Use e = : 2.7).

Q: 3. (8x³ + 6x²5x +11) dx

A: integration

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A: Let's find area under the curve by using two rectangles.

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A: if a vector is of the form  a→=a1,a2  then a→=a12+a22 see  below the answer

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A: Since you have posted multiple question which is not interlinked i can do first question as per our…

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A: Let's solve.

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A: We know that derivatives of xn is nxn-1. And d(tan-1x)/dx = 1/(1+x2).   Here i attached the solution…

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Q: 7. Prove that: (3) (a) (4) (b) sin20 cos20-1 in (-0) + cos (- 0) = cost -cote =

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Q: (a) By separating the variables and integrating, solve the following initial value problem:…

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Q: Q5/Change the polar equation 2r = 2 + cos8.(2r - 1) to Cartesian equation

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Q: 15 //dx Sº

A: Topic:- application of integration

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Q: Consider the initial value problem x' = 4x², x(0) = x0. For what value(s) of co will the solution…

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Q: ринд (((-15)75] Thin 256 - уч 니 e ठेपण

A: We have to find value of given Integral.

Q: Q1. Find the half-range sine and cosine Fourier series for f(t) = t in each case. 0 < t < 2. Draw…

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Q: Use the graphs of f and g to evaluate the function. y=f(x) y=g(x) Exercise (a) (fog)(3) Step 1 Note…

A: Use the graphs of f and g to evaluatethe function. Exercise (a) (fog)(3)

Q: What function will you differentiate to get each function? 3. g(t) = -3t2 + 12t - 17

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: 2. Find the differential equations by eliminating the arbitrary constants of a) y = C₁x + 2² b) y ex…

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Q: x² dx x²-3x+2

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Q: B. Find the volume of the indicated solid i) under 2x - 3y + z = 6 and above the rectangle R = =…

A: Let's find volume of solid(V).

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Q: Numerical Response #4: A close who will get to ride to grad in an girls in the limo then there are

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Q: - be to your advantage to simplify first.

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Q: 8 For the function y = f(x) = 7+2²' a. Find the slope of the line tangent to its inverse function at…

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Q: Mark on an Argand diagram the points representing the following numbers: (a) 2 (b) 3i (c)-i (d) 1+2i…

A: Plotting the given complex number in argand plane

Q: Find the average rate of change of the function y = 2e2 with respect to x over the interval from x=0…

A: As we know that; The average rate of change between the interval a≤x≤b is given by; Avereage rate of…

Q: What function will you differentiate to get each function? 1. f(x) = 4x³ - 6x² - 10x + 1

A: Given function is:

Q: Determine L-1. 2s² +10s (2s²-20s+58) (s+1)

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Q: Find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius…

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Q: Find a function f such that for any real number x such that 2√x + tan-¹x In csc x [₁₁ (1) dr = 3 +…

A: To find a function f such that for any real number x such that ∫-1xft dt=2x+tan-1 xlncsc x+π

Q: Evaluate the integral. (Use C for the constant of integration.) /1+√x ox dx

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Q: 6. Compare and contrast the properties of the 1st Derivative of various functions with its 2nd…

A: The first derivative is the slope of the function, and the first derivative test is used to find the…

Q: Numerical Integration. Use the table provided for the integral to find the given ap Round each…

A: Given ∫141x We need to find the trepizoidal approximation for 6 sub-intervals∫abf(x)…

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Q: 3) 2x (1+y²) dx -y (1+2x²) dy=0 4) dx + x lnxlny dy =0

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Q: Expand f(x) = 3x as a half range Fourie.....sine.... series in the range 0.₁FX.. F... ..ans.: f(x) =…

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Q: 9. 10. If f(x)=√ex, the derivative is: √ex a) f'(x) = Vex b) f'(x) = √ex c) f'(x) = 2x Which of the…

A: Calculate the derivative of both problem in the following way:

Q: the convergence and divergence of the following S vergent series. b) Σ=13*51-n

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Q: 3. Given the equation y = x³ - 3x² + 3, determine all Critical Points and classify using the SECOND…

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Q: 8 1 1 -dx אן

A: If the integral gives finite value , it means integral converges otherwise diverges.

Q: Juliana invested $5,100 at 5.50% p.a. simple interest. How many days will it take for her investment…

A: Given :Juliana invested : $5100Rate 5.50% p.a.Grow up to $5310

Q: Q1) Test the convergence and divergence n 1) {( {1}}=1 n+1 210 – Vn 2) Σ n2+n+2 n=0 8 6n² 3) Σ n³ +1…

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