1. Evaluate the following integral: S (t² + 3) cos(5t) dt (Note: Take a and b any two numbers of your MEC ID number, with a condition that a < b. For example if your MEC id no. is 16f23450, take a is 0 and b is 1 or a is 1 b is 4 like that.)

Q: Define the following improper integrals.

A: a). The improper integral functions.

Q: 3 Is x + 2 a factor of a* + 3a* - Зх — 10? Select an answer O The remainder when you divide is Is 2x...

A: 1) Check whether  x+2 is a factor of the polynomial by dividing x3+3x2-3x-10 by x+2. For that use th...

Q: Determine the following indefinite integral. Check your work by differentiation.

A: ∫3u-2-4u2+1 du=3·u-2+1-2+1-4·u2+12+1+u+C   ∵∫xn dx=xn+1n+1+C=-3u-4u33+u+C

Q: Which of the following defines a function f for which f (-x) =- f (x)? Select one: f (x) = log.x a. ...

A:

Q: If the function f(x) = {cos(2πx−a),x&lt;−1x3+1,x≥−1 is continuous, what is the value of a?

A: fx=cos2πx-a,  x&lt;-1        x3+1,    x≥-1 Since Cosine function is continuous for all real numbers,...

Q: Suppose the functions f, g, h, r and l are defined as follows: f (x) logs + log, r g (x) V(x - 3)2 h...

A: As per the bartleby guidelines from more than one part only one has to be solved. Please upload the ...

Q: 1 If y = tanu, u=v--, and v= lnx, dy at x=e? dx what is the value of Select one: a. 0 O b. 1 1 C. d....

A:

Q: The integrals converge. Evaluate the integrals without using tables

A: Evaluate: ∫-11 dxx23

Q: Differentiate the function   f(x) =    x / ex

A: Derivative of the function fx=xex

Q: Prove that if a is an upper bound for A, and if a is also anelement of A, then it must be that a = s...

A: We have to prove that if a is an upper bound for A, and if a is also an element of A, then it must b...

Q: If f is increasing and f(x)>0 on,/, then g(x)%=1/f(x) is decreasing on I. Select one: O True O False

A: Follow the steps.

Q: How can we represent a function ?

A: Function is the relation in which each element of the domain is related with exactly one element in ...

Q: It is possible that functions f and g are not continuous at a point x0 but f+g is continuous at x0. ...

A: Given that f and g are not continuous at a point but f+g is continuous at x0 . This statement is Tru...

Q: Use the definitions of right-hand and left-hand limits to prove the limit statements in Exercises 53...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: Fill in the blank/s: The formula for nCr has the same numerator as theformula for nPr but contains a...

A: We have to fill in the blanks: The formula for Crn has the same numerator as the formula for Prn but...

Q: The area bounded by the curve y = x*, x- axis and the lines x=1 and x=2 is_ O A. 21 5 О в. 31 5 ос. ...

A:

Q: a. Find the absolute maximum and minimum values of each functionon the given interval.b. Graph the f...

A: Given: fx=1x+lnx, 0.5≤x≤4 for finding absolute maximum and minimum values of given function, we draw...

Q: Use cylindrical shells to find the volume of the solid. right circular cone with height h  and base ...

A: We consider a right angle triangle OAB. Whose vertex O is at the origin and base OA is along the x-a...

Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose volu...

A:

Q: The pressure in P = 10T/V     of a gas in a cylinder is given by   with T in kelvins (K) and V in m3...

A: Given : P = 10T/V

Q: The graph shows the height, in meters, of an eagle in terms of its time, in seconds, in flight. a. I...

A: (a) - Yes, the eagle's height is a function of time as per the graph shown.We see that as the time i...

Q: Find the limits

A: Consider the given limit, limn→∞1n+1+1n+2+⋯+12n now write the limit in the summation form, limn→∞1n+...

Q: Find dy dx2 Q2 when t = 1 if given the parametric functions as below, x = 3e5t y = te-5t

A:

Q: 1. For the function h(x) whose graph is shown, find the values of x such that the derivative is posi...

A: (a)Given that,h'(x) &gt; 0Here, derivative is positive.When derivative is positive , the function is...

Q: Find two vectors in opposite directions that are orthogonal to the vector        u = ⟨3, 1, −2⟩

A: u=3, 1, -2 Let v=a, b, c be the vector orthogonal to the vector u=3, 1, -2. Then, u·v=0             ...

Q: The following initial value problem model the payoff of a loan. In each case, solve the initial valu...

A: The differential equation is  B't=0.004B-800 with the B0=40000.

Q: Sketch the region bounded by the graphs of the equations f(x) = x5 + 2,      g(x) = x + 2 and find t...

A: Consider the given equations, fx=x5+2 and gx=x+2 the graph of the equations on the same coordinate a...

Q: Express the vectors in terms of their lengths anddirections. -i - j

A: Given vector is: v = -i -j Then we get, The magnitude or the length is: = sqrt{(-1)^2+(-1)^2} = sqrt...

Q: Evaluate and simplify y′. y =12x - 32x3&gt;2

A:

Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area amo...

A: Given information: V=64 m3