1. Find all the values of a, b e R such that the function sin (3x) ax is continuous. if x > 0 if x = 0 (arctan (¹) if x < 0 f(x) = { b

Q: 10+ 8 6 4 2 -6 -5 -4 -3 -2 -1 -2 -4 -6- -8- -10 1 2 3 4 5 The function graphed above is: Concave up…

A: We solve the given problem by using the second derivative

Q: Sketch a graph that possesses the characteristics listed below. f is increasing and concave up on…

A:

Q: f(x) = 4x5 - 5x4; x = 1

A: f(x)=4x5−5x4Using the power Ruleddxxn=nxn−1

Q: Melissa has savings in two different accounts: she has $6,700 dollars in an account that pays an…

A:

Q: 1 0.8 0.6- 0.4 0.2 3Q Use Newton's method to approximate a root of the equation cos Enter your root…

A: We have to use the Newton's method to approximate a root of the equation

Q: 3. Determine whether the series converges or diverges. If it converges, find its s 3n+1 ∞ ∞ (a) (b)…

A: Find whether  series  converged or diverges

Q: Find f'(x) in two ways: (1) using the product rule and (2) simplifying first. f(x)=x²(x²-5) Which of…

A:

Q: For the following exercises, solve to four decimal places using Newton's method and a computer or…

A:

Q: f(t) = sin²(t)

A: Formula for find laplace transform of f(t) L[f(t)] = ∫0 ∞ f(t) e-st dt ∞ f(t) e-st dt

Q: Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand…

A:

Q: Q.4 Find all second order partial derivatives of f(x,y) = sin(xy).

A:

Q: 25. A jar contains 12 differently coloured balls. If you remove the balls by taking two balls, one…

A: find the number of colour sequences possible in given question.

Q: The number of visitors P to a website in a given week over a 1-year period is given by P(t) = 123 +…

A: According to the given data, we have

Q: Find the equations of all tangent lines passing through the point P (− 2, 8/3) and tangent to the…

A:

Q: 13. g(t) = 215(0.95) 14. h(x) = 7(1.025)

A: The given functions are 13. 14.

Q: When converted to an iterated integral, the following double integral is easier to evaluate in one…

A: The double integral of xsec2(xy), y from 0 to 2 and x from 0 to pi /6

Q: The speed of a car at time t, 5 ≤ 1 ≤ 10, is given by f(t)= 2(t-10)². The Mean Value Theorem…

A: The speed of a car at time  is given by  The mean value theorem gaurentees that there will be a…

Q: What is the average value of f(x) = (sinx)15 Cox for the closed interval 0 ≤x≤ 플? Select one: 0 a.…

A:

Q: Find the length of the curve: y = 0 < x < 8 3 x

A: Given function of the curve,

Q: 2 (α) Σ 4n² - 1 n=1

A:

Q: 28. A jogger jogs every morning to her coffee shop, which is 7 blocks east and 7 blocks north of her…

A:

Q: dx Assume that x = x(t) and y = y(t). Let y = x³ +5 and 4 when x = 1. dt Find 315 11 dy when x = 1.…

A:

Q: ∞ (d) Ene-n? n=1

A: We have to determine whether the series converges or diverges.…

Q: Determine the vertex of the parabola without graphing. f(x)=2x²-12x+18

A:

Q: Use the Second Derivative Test to find the location of all local extrema in the interval (-6, -1)…

A:

Q: Consider the function f(x) = x + 2 cos x, for 0 < x < 2п. Which of the following values are…

A: we need to find out the inflection points for the given function on the given intervals.

Q: 17. x -2 h(x) 12 -1 0 1 15 16 15 2 12

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: What is the slope of the line tangent to the curve X = (1 + sin t) cost, y = (1 + sin t) sint at t =…

A: x=(1+sin⁡t)cos⁡t,y=(1+sin⁡t)sin⁡t at t=π

Q: 1 2 The curve given by x=√₁²-y² where -a ≤ y ≤a; is rotated about the y-axis. Find the resulting…

A: The curve is rotated about the y-axis.

Q: Consider the function below. (Round the answer to two decimal places.) f (x) x+7 x² +7 (a) Find the…

A:

Q: Use an X [√² X appropriate substitution and then use a -dx trigonometric substitution to evaluate…

A:

Q: Determine whether the equation is exact. If it is, then solve it. 2t dy + (2 In y + 5)dt = 0 ....…

A:

Q: Consider f(x) = −11+14x² 8x + 12x³ and use the Second Derivative Test to address the following…

A:

Q: Given f(x) = x² + 3x + 9, find the average rate of change of f(x) over each of the following pairs…

A:

Q: Evalutate the double integral by reversing the order of integration. Integral from 0 to 27,…

A: Step 1: The region of integration is bounded by the curves y = 0, y = 3, and Step 2: Reverse the…

Q: Find the indicated derivative. dz | dx dz dx = x² for z = + x² 1- x - 3x²

A:

Q: Suppose y = √2x + 1, where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4. dt…

A:

Q: This exercise is based on the following table, which lists interest rates on long-term investments…

A: The formula  Initial amountAmount at time tRate of interestCompounded period Time in years

Q: Question 5 If g is differentiable, then [9 (√)]: O True False Question 6 If y = e², then y' = 2e.…

A:

Q: tanh(In(x)) tanh(In(x)) : x² - 1 x² + 1 cosh (In(x)) 1) - (x34²) - 1 +1 2 eln(x) + e X+X X + X (x² +…

A:

Q: Express the series n=1 1 x 2n as a rational function.

A:

Q: If [²F f(x) dx = 37 and So g(x) dx = 18, find S [3f(x) + 5g(x)] dx.

A: For ,  as both integrals have same limits.and

Q: Find the derivative of the function f(x): Provide your answer below: f'(x) = = X 2 -4 T

A:

Q: Find the limit. Use I'Hospital's Rule where appropriate. If there is a more elementary method,…

A:

Q: Given f(x) = f'(2) = 1 x+1 find f' (2) using the definition of a derivative. Provide your answer…

A:

Q: Question 3 Consider the piecewise defined function given in question #2. Discuss the continuity of…

A: By the graph of a function we can say, the function f(x) is continuous on an interval [a,b], if…

Q: y' + y" = 2x²y 10y' - y = ex 2 tanh(y)y′ +2xy+3=0 y” = tanh(y/x)

A: To define whether each of the following ODEs are 1st-order linear, 1st-order non linear,2nd-order…

Q: Write the quantity using sums, differences, and constant multiples of simpler logarithmic…

A: The objective of this question is to simplify the given logarithmic expressions using the properties…

Q: The following linear system is in echelon form. Solve the linear system by back substitution. X₁ -…

A: The  following linear system is in echelon form. To solve the linear system by back substitution.

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

A: Since you have asked multiple sub parts in a single request so we will be answering only first three…