Compute the following limit.“ KC'arctan(2t³ – 1) dt] du (x – 1) In r lim Be sure to explicitly explain and justify every step of your work for this problem. For example, if you have to evaluate any limits during the course of solving the one above, explain exactly why you are able to evaluate it. If you have to apply a theorem, explicitly justify why you can use it (i.e., check its hypotheses). “

Q: Use the graph of y = f(x) shown below to answer parts a) through c). Mhesh F J K E f(x) X a)…

A: 1. We know that the derivative of a function represents the slope.   2.At the point of local…

Q: Apply the Golden section method with x, = 3 and X, = 4 %3D to locate the maximum of f(x). Take &,…

A:

Q: 3. Consider the function f(x) = e" on (0, 2), and a point a e (0, 2]. Consider the triangle formed…

A: Given function f(x)=e-x on [0,2]. The objective is to find the point a such that the triangle has…

Q: 2. what is the domain of the function)

A: Given function is, f(x,y)=cos-1x2+y2-3+lnx2+y2-3 The graph of the function is,

Q: 2. Approximate v1.02 +0.02 using an function f(x)=√x + 1 + e*. appropriate local linear…

A:

Q: Use the graph of y = f(x) shown below to answer the following questions. If f does not have a…

A: The graph of y=f(x) is

Q: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: exp(x) — еxp(-ӕ) f(x) = + In(x) exp(x) + exp(-æ) wherer e [1, 5). Use 5 nodes to uniformly cut the…

A:

Q: 1. Consider finding the root of f(x) =x´ – 5 use secant method, ɛ = 0, and start with the a interval…

A: given , f(x) =x2 - 5  we have to find roots of f(x) in interval by using secant method

Q: 11. Find the absolute maximum and minimum values of each function on the given interval: (a) y =…

A: The given functions

Q: 2. a) f(t)=2sin(t), -2, 0≤t<π/2 π/2 < t < 3π/2 t≥ 3π/2

A:

Q: The graph of ƒ is given. Let and evaluate A(2), A(5), A(8), and A(12).

A: From the given Figure, a. A2=∫02ftdt=-14 of circle of radius 2=-14π×22=-π   b.…

Q: 2. Find the vertical asymptote/s of 7.x f(r) : %3D x2 - 3r- 28'

A: Here we have to find the vertical asymptote of the function f(x)=7xx2-3x-28

Q: s of stick t

A: Given that it needs 5meters of stick to make a picture frame.

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: The slope of the tangent line to the graph of the function y=3V-4at (16,8) is 16.00 4. -1.00 O-0.50…

A: Now,

Q: Sr*y" – 4ry + by = 0 y(C) = D, y(C) = U – 1

A:

Q: Find the exact absolute maximum and absolute minimum of h(t) = cos(2t) + √3 sin(2t) on [0,1]. Show…

A: h(t)=cos(2t)+3sin(2t)for critical points, put h'(t)=0d dt(sint)=costd dt(cost)=-sint

Q: 2. Let g(x) = "(x² – 4x + 6) dx. Is the graph of g concave up or concave down at x 1? Justify your…

A: Explanation of the answer is as follows

Q: x2+1 is: 15. The slant asymptote of f(x) = is: x+3 %3D A) y = x. B) y = x – 3. C) y = x + 3. D) y =…

A:

Q: gixl= f, f(t)dt, where f is the fun ction whose graph is shown.

A: Given : The graph of f(t) is given

Q: 4. Find the differentiation dy. using definition with limit of the following: y = V2x + 1.

A:

Q: x²+3x (t – 1)e' dt 2л — 4 - lim x→2

A: Given limit is : limx→2∫10x2+3xt-1etdt2x-4dt To find the value of limit by using L’Hospital’s.

Q: Sx² – 1, (2x + 1, 3 < x < 10 x< 0 Evaluate lim f(x) if f(x) = x→3

A: Since left and right limit at x =3 not equal then we say that limit does not exist at x=3

Q: f(x) = 2 +7 cos(x), 0 ≤ x ≤ 2π

A: The given function is

Q: x²+4 Let: f(x)= x² -4 - 16x 16(3x²+4) - f'(x) = f"(x)= %3D (x² – 4)² ' 1. Find x- and y- intercepts…

A:

Q: f(x) = - [x + 1 for xs0 lx -1 for x > 0 a. Show that f(-1) - S(1) = 0 but that there is no number c…

A:

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…

A: