Find the equations of the tangents to the curve x = 9t2 + 9, y = 6t3 + 6 that pass through the point (18, 12). y = -x + 30 (smaller slope) y = x – 6 (larger slope)

Q: If the derivative dx (instead of .) exists at a point and dx = 0, then the tangent line at that…

A:

Q: a) [. :l: Determine whether the following series (-1)"5"-1n . 42n+1 n=1 is convergent or divergent.…

A: As per policy only first question is answered. Please refer to the image below

Q: FEx) = 1+e siny x fCx) f'ca) = fco) = - fくb) = fCl-2) = = -15 e sin4X- se"cos4X 8 LN %3D %3D %3D…

A:

Q: (2 C/2x-x² 30. Vx² + y? dy dx Jo

A:

Q: Evaluate the integral given. sec(2a)tan(2a)dx +C %3D

A: ∫ sec(x)tan(x) dx =sec(x)+C

Q: 60 50 40 30 20 10 -10 10 20 30 Victoria is a lifeguard and spots a drowning child 30 meters along…

A: We need to find distance of jumping.

Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

A:

Q: Find the slope of the tangent line to the curve la? + 4xy – ly = 11 at the point (2, 1).

A:

Q: Suppose that f is defined everywhere and x = 2 and x = -1 are the only critical numbers for f. If f"…

A:

Q: Find all critical points of the function f(x) = sin-'(x) – 8x for –1 < x < 1. (Use symbolic notation…

A:

Q: 3 B. Find the eigenvalues. -. 2,= -1 & 1z= 4 B. A,= 2 & 12= 2 C. A,= 4 & 12= 1 E Nona

A: Topic:- matrix algebra

Q: answer

A: We will find the second derivative.

Q: What will the domain be, could you state the domain?

A:

Q: 44 3) y" +y = sec?x (Use variation of parameter method)

A: To solve the given differential equation.

Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 63°C, it…

A:

Q: A quadratic polynomial y- 4r+7r-3has roots pand g Find a quadratic g(r) o+withrots and a O a.…

A: Please see the answer below.

Q: Given f (x) = a +1 and g (x) = 2x +3, find f[g(x)]. %3D %3D O A. fg(x)] = 2a2 + 5 O B. f9(x)] = 2a?…

A:

Q: a) Test the series 7-1)" for n=1 convergence or divergence (show all your works) b) Test the…

A: We have to find series convergence test

Q: 4. Explain why (* + ÿ) + (ž + t) equals MQ in the following diagram.

A: answer is in next step

Q: - If v1, v2 are 2 vectors in a vector space V such that 0 = 4v1 – 2vz. Then{v1, v2 } are linearly…

A:

Q: Evaluate the following integrals. Use only the variables "u" (and "v" if applicable) in your…

A:

Q: In 1978, cars that got about 40 miles per gallon were readily available. If the average fuel economy…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: 1 n =1 (2n- 1)4 M8

A: Integral test

Q: graph below, whet is a pont ad which it would O Giue the function in the reas ona ble estimete…

A: The inverse function is reflation to original function at y=x

Q: Find the minimum and maximum values of the function y = 8Vx² + 1 – 7x on the interval [0, 8] by…

A:

Q: What is the absolute maximum value of the function f(x) = x – 3x2 on the interval [-2, 3] ? a. None…

A: Given the function is f(x) = x3-3x2 on the interval -2, 3.

Q: Consider the function f(x) = x2 -1 %3D (a) Find the intercepts of the graph of f (if any). (b) Find…

A: The given function is: f(x)=xx2-1

Q: Give the range of the function f(x) = -x 2. all reals y ≤ 0 y ≥ 0

A: The given function is: f(x)=-x2

Q: x = -3 is a critical number of the function f(x) = (x – 3)(x + 3)². Select one: O True O False

A:

Q: dy for the function y= Find dx (x-1)(x-2)* (x-3)' at @x = 4.

A:

Q: Not yet answered Marke Prove that f(x) = (x- 1) + (x +1)² is an even function. A function k(x) is an…

A:

Q: a) Test the series EN7-1)" for n =1 convergence or divergence (show all your works) b) Test the…

A: We have to find convergence test

Q: For j(z) = (3x2 - 7) (-2x* + 7x), find j' (x) by applying the product rule. Provide your answer…

A: j(x)=(3x2-7)(-2x3+7x) The product rule is: (fg)'=f'g+fg' From above:  f(x)=3x2-7g(x)=-2x3+7x Now,…

Q: 3. Evaluate: lim -) x-0 (sinx

A:

Q: Question 3 - a) ji following series : Determine whether the (-1)"4"-1 32n+1n n=1 is convergent or…

A:

Q: 3. Evaluate the integral. (a) -2/3 dx

A: Evaluate the integral

Q: Determine the limit: lim 4x2 x→0 sin (2x) cos(2x)

A:

Q: 06: A- A projectile is to be fired from ground at angle of 30° to reach a target point that is 100m…

A:

Q: The integral of the given function sin³x cos x dx is equal to a. 1/3 b. 1/4 с. 1/5 d. 1/6 e. None of…

A:

Q: 6. Solve the differential equation: 2xydx + (x² - 1)dy = 0 А. ху - 1- с B. x'y - y = C С. x y = C D.…

A: We have to solve the equation

Q: x2 +y? +z? - 4x + 8y – 2z = - 12

A:

Q: 3. f(x)== 4. f(x) = + 1

A: 3) f(x)=1/(2x)  4) f(x)=(2x-4) /(3x) +1

Q: The function x2 f(x) 1 - x | has a local maximum when x = 2. Select one: True OFalse

A:

Q: a) Determine whether the series (-1)"n² 00 Σ is convergent, n3 + 3n + 1 n=1 absolutely convergent or…

A:

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

A:

Q: Eliminate the arbitrary constants on the given equation: y = Ae + Bxe" O y = y' – 2y O y' + 2y +y =…

A:

Q: drop of oil in the shape of a circle is increasing its area at a rate 4 cm2/min. Find the rate of…

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

Q: 3. Two vectors, à and b, have a common starting point with an angle of 120° between them. The…

A: Solving

Q: Use the definition of continuity to show that h(x) = x^2 + 5x/2x + 1 is continuous at the number a…

A: The given function,   h(x)=x2+5x2x+1

Q: a. For the given value of n, use sigma notation to write the midpoint Riemann sums. f(x) = cos 2x…

A: