Question 14 <> Use part I of the Fundamental Theorem of Calculus to find each derivative, given the following f(x): 1 dt 1 + t2 f(x) 1 f' (x) = 1 + x2 1 f'(12) = 145 > Next Question

Q: 5. Given y = af(+ 1), Find when x=1 if f(2) = 4 and f'(2) = 5. dx

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Q: 3. Evaluate: lim X-0 \sinx 4. Using the binomial series, find the power series of f(x) =

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Q: 2. Determine the area of the region bounded by the curve y = x³ – x2 – 2x, and а. the x-axis b. the…

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Q: B. Find the value of x for which Inx + (Inx)2 + (Inx)+ (Inx)* + = 9

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Q: Consider the function f(x) = x2 -1 (a) Find the intercepts of the graph of f (if any). (b) Find the…

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Q: All exponential functions can be written in many forms. Write the function f(t) = 620e0.35t in the…

A: We have to transform the given function in given form function.

Q: Suppose a curve is defined by the equation 16(x² + y²) = 45. Show that if you translate the curve to…

A: we have to translate the curve.

Q: 7 - 3 - | 87 23 Find the eigenvectors of the given matrix: 土 i

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Q: (4) Consider a product whose unit cost is $3/item and whose demand function is given by 50000 D(p) =…

A: Profit function: Subtracting the cost function from the revenue function yields the profit function.…

Q: The polar coordinates of a point are given. Plot the point. 57 T/2 T/2 3 2 2 -3 -2 -1 1 2 3 -3 -2 -1…

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Q: 3. Evaluate: lim -) X-0 \sinx 4. Using the binomial series, find the power series of f(x) = =

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: How did he get the second derivative step by step and a clear line please 3 -X- Fex) = I+e sinu x…

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Q: Solve the differential equation below using series methods. y'' – 4xy' – y = 0, y(0) = 4, y'(0) = 2…

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Q: The velocity of an object moving along a line is given by v = 3t2 + 1 ft/s on the interval 0sts4. a.…

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Q: (iii) Find the angle between the vectors. a = 8i – j+ 4k, b= 4j+ 2k (iv) Find the volume of the…

A: Given a=8i-j+4k, b=4j+2kTo find angle between two vectors:

Q: 3. x = y? ,x = -2y² + 3

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Q: lim x? O1 -25 25 -1 ||

A: The detailed solution is given below Thank you

Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: The answer is not -900. Please give me the correct answer.

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Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

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Q: Find the equation of the tangent and the equation of the normal to the curve y = x + - at the point…

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Q: Please do help me with this calculus questions. Please. I need the correct letter of the answer and…

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Q: Рreview iv. g(0) = Preview v. lim g(x) = Preview T -1 vi. lim g(z) =L Preview %3D T-1+ vii. lim g(z)…

A: limx→a f(x)=L if and only if limx→a- f(x) =L=limx→a+ f(x) .

Q: 1. Solve the initial value problem 2 = x? – 1, y(3) = 7. dx

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: ^2/sin^2(2x-6) = -1 since sinx/x =1? then limit is like x^

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Q: n lim (5(x;) – 3(x;)*)Ax over [0, 2] i=1

A: To convert this limit of sum as definite integral over given interval.

Q: For the points P1 (4,8,7) and P2(5,7,6), find the direction of P,P2 and the midpoint of line segment…

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Q: Differentiate exp(sec(x^2)

A: Given query is to find the derivative of the expression.

Q: if f(x)=(5+x4)1/4 what is (f(x))2

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Q: Find two sets of polar coordinates for the point for 0 s0 < 2z. (r, 0) = (smaller r-value) (r, 0) =…

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Q: Зx+2 11. Evaluate: S -dx. x3-x2-2x Solution:

A: To evaluate: ∫3x+2x3-x2-2xdx=∫3x+2x(x2-x-2)dx=∫3x+2x(x-2)(x+1)dx

Q: Determine the linear approximation of f(x) = x* at x = 1. а. у %3D 4x - 3 O b. y=- 4 x - 3 О с. у-…

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Q: -2 is a critical number of the function - Vir - f(x) = 2x x2. Select one: True False

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Q: What are the first three non-zero terms in the Maclaurin Series of f(x) = e* sin(x)? x - +-- О а.…

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Q: 5-6 Sketch the region whose area is given by the integral and eval- uate the integral. 5. ". 2 (7…

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Q: Let u = 8i + 2j, v=i+j, and w =i-j. Find scalars a and b such that u = av + bw. a = b =

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Q: - Solve the differential equation y-2y'+y e" In x

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Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

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Q: 75° 4 A = (b) 0.4 rad 15

A: Given, theta= 75° Radius(r)= 4 units We know that, Area of sector= (theta/360°)×(pi×r²) Substituting…

Q: 5. f(x) = 2x + 3

A: First write the formula and then put all the values and simplify.

Q: 6. Verify each of the following identities: cosx (a) 1-sinx = secx + tanx (b) 2sec²x + 1+sin 1-sinx…

A: As you have asked for question d only. So I am solving that only. Thank you.   sec(x)*cos(x)=1…

Q: Find the length of the curve over the given interval. Polar Equation Interval r = 8a cos 0 16 16.

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Q: Plane travels for 9.5 hours on two-way trip between location A and B. The Plane can fly at 320 km/h…

A: Plane travels for 9.5 hours on two-way trip between location A and B. The Plane can fly at 320 km/h…

Q: the distance between point and our plane is (-3, 3, -2) and not (-3, -3, -2)?

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Q: Checking using Second Derivative Test

A: From the secon derivative test, if the value of second derivative at the critical point turns out to…

Q: -7 -3 A 87 23 Find the eigenvectors of the given matrix: -.1 1 1 i 3 - 15

A: Solution

Q: Consider the function f(x) = x2-1 (a) Find the intercepts of the graph of f (if any). (b) Find the…

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Q: where did you get 9.9999

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Q: Write the sequence in recursive form. Make sure to state the initial conditions a, - 4(3)" for n > 1

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Q: Using binomial expansion, write down the first three terms of the expression below, starting with…

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