i) State the change-of-base formula for logarithms. ii) Using the change-of-base formula, and the natural logarithm functionality on your calculator, compute the following, accurate to 6 decimal places: a) log7(12) b) log2(18) c) log4(7:32)

Q: | 3te2t dt Answer:

A:

Q: Using the figure shown, find sece (3,- 4) 5/4 5/3 -5/4 -5/3

A:

Q: Given: (-8, 6) cote = -3/4 O 4/3

A: Find your answer below 

Q: The Differentiation to be made must be based on the following topics. - Trigonometric Give 3 example...

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) cos 5 t dt COS V sin t

A:

Q: Use the shell method to set up a definite integral (set up only, do not evaluate the integral) for t...

A:

Q: A rocket is launched from the ground at an angle measuring 0.69 radians. The rocket travels in a str...

A:

Q: 2r (1- lim

A:

Q: Find the volume of the solid obtained by rotating the region petween the curves y = 3x - x³ and x-ax...

A: Given query is to find the volume of the solid generated.

Q: 1. Find the y" of y (4x-3x + 1)9 (5x + 7)2 1/2

A:

Q: 1. A soccer ball is kicked 20m/s at an angle of 30° above the horizontal. Determine the horizontal a...

A: Using trigonometric find horizontal and vertical components

Q: For the following function, a) give the coordinates of any critical points and classify each point a...

A:

Q: For f(x)=√(x^2+2) find all the values of c on the interval [0, 1] that satisfy the Mean Value Theore...

A: Given query is to apply mean value of theorem and find value of c 

Q: Test the series for convergence or divergence using the Alternating Series Test. in 2(-1)"- n° + 7 n...

A: Given query is to find the series converges or diverges.

Q: Using appropriate substitution, the integral S e t3 dx is equal to:

A: ∫ex-3dx/x4 now substitute u = x-3 du/dx = -3/x4 dx = -x4du/3 ∫ -eudu/3 (-eu)/3 + c now put value of ...

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A:

Q: One measure of living standards in country A is given by the following formula. L(t) = 5 + 4 e 0.16t...

A: Given: One measure of living standards in country A is given by the following formula.L(t)=5+4e0.16t...

Q: Question 6 of 9 Find the Taylor polynomials of orders n = 0, 1,2, 3, and 4 about x = x0 and then fi...

A:

Q: Find the radius of convergence and the interval of convergence. k(k + 5) k=1 Radius of convergence: ...

A:

Q: Identify the problem whether a Permutation or Combination. Write the given of the problem and solve ...

A: Permutations and combinations

Q: 2. Find the derivative for each of the following, be sure to use proper notation and simplify when n...

A: As per guidelines I can only solve first three subparts , remaining can be reposted

Q: 5. Use the integral test to determine the values of p for which the series below will converge. 1 k(...

A: Here we have to use the integral test to determine the value of p for which the series below will co...

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 3 %3D

A:

Q: Assume that a rectangle with sides x and y is changing with time. Let y = 2x and x(t)=t^2 What is t...

A: Given query is to find the rate of change of area.

Q: 7. Given vectors ū =[2,1,4], v =[1,2,–1],and w=[x,1, z] find x and z such that ū x w = v.

A: u ×w = v now u × w = i    j    k                      2   1   4                      x   1   z now  ...

Q: Use the formula for the binomial series: m(m-1)2 + 2! m(m-1).(m-k+1),k + .. (1 + x)" = 1+ mx + ... k...

A:

Q: The Differentiation to be made must be based on the following topics. - Power Rule Give 3 examples w...

A: It is required to give three examples with solution and final answer on differentiation using power ...

Q: Determine whether the given series is convergent or divergent. Justify your answers. +00 (2n)! 2(n +...

A:

Q: Q5) A) Graph the curve Y = - 2 x (x - 4)(x + 6)(x - 2) between the value of x [0, 4), then find the ...

A: To graph the curve y=-2xx-4x+6x-2 between the value of x in the interval 0, 4, then to find the area...

Q: x = -1 if y=u° +5u – 4 a

A:

Q: A person coughs when a foreign object is in the windpipe. The velocity of the cough depends on the s...

A:

Q: Question 2: Differentiate the functions by using product or a) f(x) = (3 – x²)· sin5x

A: Given: a)f(x)=3-x2sin5xb)f(x)=3cosxx-5

Q: The Differentiation to be made must be based on the following topics. - Quotient Rule Give 3 example...

A:

Q: Let the height of an object bef(t)=t2+2t−4f(t)=t2+2t−4. What is the instantaneous rate of change of...

A: Given query is to find instantaneous rate of change of the object at t = 2.

Q: Q3) Evaluate the following integrals: sec(tan-1x). tan³ (tan-1 x) A) y = S dx 1+x2

A:

Q: What dimensions will maximize the lateral surface area of an inverted cone, if V = 27 cm³?

A:

Q: Question 6 Find the derivative of the function y = 8ln(cos 2x)+ 5tan? (3x) Write the value of y' (0)...

A:

Q: Find the max emin, nflection Points and the in ter Vals on which the function iiHereaserdecrease con...

A: Given query is to find the the key points of the function.

Q: Use polar coordinates to calculate the volume of a sphere of radius R.

A: This question is based on application of polar coordinates integration.

Q: 3 - 2x? +x- 2 Use L'Hopital's Rule to evaluate Support your answer graphically. lim X2 x² +x-6

A: To find: The limit by L'Hopital rule. Given information limx→2x3-2x2+x-2x2+x-6

Q: 2. Find the derivative for each of the following, be sure to use proper notation and simplify when n...

A:

Q: Using the figure shown, find tang

A: Here we have to use the figure to find the value tanθ=?

Q: Use L'Hopital's Rule to evaluate the exact value of lim(x² – 2x+1)*-1.

A:

Q: The derivative of the function y = x(tan-'(3x))² is: y' tan (3x) 6x + (1+9x²) tan-³(3x)] tan (3x)[6x...

A: y = x(tan-(3x))2 dy/dx = (dx/dx)(tan-(3x))2 + x(2(tan-(3x))(3))/((3x)2 +1) dy/dx = tan-(3x))2 + 6x(t...

Q: Find the indefinite integral. x2 + 8x + 5 x3 + 12x² + 15x + 6 xp

A:

Q: Minimise x + y - 2xy subject to the constraint y 1: Answer:

A:

Q: 4. For vectors ū and î as shown, a) Determine the magnitude and direction of üxv. 10 145° 8. b) Dete...

A:

Q: Confirm that the integral test is applicable and use it to determine whether the series converges. 1...

A:

Q: 00 4n + 15-n Untitled n = 1 5.5 5.5 Upda Determine whether the geometric series is convergent or div...

A: Topic:- sequence and series

Q: 12. Simplify the following rational expression for the function f (x) = 5x2 f(x + h) – f(x) h

A: Given f(x)= 5x² So, f(x+h)= 5(x+h)²=5x²+10xh+5h²