The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 150 cm2?   --------- cm/min

Q: . Determine the area below f(x) = 8x - 2x² and above the x-axis.

A:

Q: Amount of error  Percent of error

A: Given ,  1 cubic inch = 16 cubic cm  True value :  1 cubic inch = 16.39 cubic cm We have to find…

Q: Find a tight upper bound for the approximation to * cos(z) cos(x) Note that the second derivative of…

A: Concept: Midpoint rule: Assume f(x) is a continuous function on [a,b]. Let n be a positive integer…

Q: du (A) Show that if y=csc(u), then=-csc(u) cot(u) dx dx

A: Given :y=csc(u)Proved

Q: Given that f(-10) = -0.1 and f(-9.6) = 1.8, approximate f'(-10). f'(-10) ~ ≈ 94

A:

Q: 2 ( D° _ 2D - 20 - 3D - 2) y = 0 = 9

A:

Q: 1. f(x) da converges, then If f(x) ≤ g(x) for all z in [a, +∞o) and converges. g(x) dx also

A: Given

Q: Find all values of k, if any, that satisfy the equation. Enter the exact answer(s). 4 0 [22 k 40 = 0…

A:

Q: .. Find the derivative of each of the following functions:- 1. y=(sin ¹x²+ 1+tan x

A:

Q: ind the indicated partial derivatives of the function. (a) f(x,y,z) = xy + 2yz +3zx+xª; ƒx‚ ƒy [(b)…

A:

Q: Find the derivative of the trigonometric function. y = cos((?x)8)

A:

Q: Suppose u and v are any vectors in R³. Which of the following is not true? Ollu + vll ≤ llull +…

A: To find which of the following properties is not true.

Q: 3.y" + 6y + 8y Pros Зе 2х + 2x

A: Let's solve given diffrential equation.

Q: Find the derivative of the trigonometric function. y(x) = cos(sqrt(sin(cot(pi*x))))

A:

Q: Find the derivative of the trigonometric function using the chain rule. y(x) = cos…

A:

Q: 5. 6. tan x dx \cos x (1/2-√√x) dx HIM

A:

Q: so ne dx

A:

Q: Let f(x) = 8x²(x-2) + 15. Find the critical points c that correspond to local minima. (Use symbolic…

A:

Q: Which of the following describes the graph of the polar equation r = 2 − 4 cos θ? (a) A limacon…

A:

Q: Determine the points (x, y) where the graph of the given equation has horizontal tangent lines.…

A:

Q: 3 4 3η ΣΣ (+1) j=1 k=0

A: A detailed solution is given below.

Q: The sum of two positive real numbers x and y is 12. Find an x and y among these such that the…

A: The sum of two positive real numbers x and y is 12.

Q: Evaluate the following: 1. [ sinh(4)dæ

A: Application of integration

Q: Use linear approximation, i.e. the tangent line, to approximate 101 as follows: Let f(x) = = and…

A: We need to find value using linear approximation.

Q: 6. S²2 (+1/12 - √x) dx

A:

Q: Find the coordinates of the vertices of the polygon after the indicated translation to a new…

A:

Q: Find the nth Taylor polynomial for the function, centered at c. 1 f(x) n = 4, c = 2 +2² P4(x) = = =

A:

Q: The linearization a at a = 0 to √8+7x is A + Br. Compute A and B. A B=

A: To Find: Linearization for fx=8+7x at a=0

Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and ƒ'(0) = 8,…

A:

Q: 1. A parallelepiped is defined by vectors à = (2,-5, -1), b = (4, 0, 1), c = (3,-2,-2). What is the…

A:

Q: Suppose that 5 J of work is needed to stretch a spring from its natural length of 24 cm to a length…

A:

Q: Find the surface area generated by revolving the curve x=y³²-y about the y-axis for 1≤ys 3/2 1/2 3

A: Solve the following

Q: 5. A ball of mass 2 kg is dropped from rest in a viscous fluid, the resistance of which is 0.001v N…

A: By solving differential equation

Q: Find the root of f(x)=(x^2)-5, in interval [0,4] by using bisection method.

A:

Q: Solve the following matrix equation for a, b, c, and d. b b + c 2 [ad - [10²] = 3d + c 2a - 4d 11 6…

A:

Q: Find the slope of the tangent line to the graph of f(x) at the point (1,2). The function is…

A:

Q: All exponential functions can be written in many forms. Write the function -0.08t f(t) = 340e- in…

A:

Q: Q5: (A): Finding a curve whose slope at the point (x, y)is 3x² if the curve is required to pass…

A:

Q: Find the nth Taylor polynomial for the function, centered at c. 1 f(x) n = 4, c = 2 +2² P4(x) = = =

A:

Q: 2. Determine which line is perpendicular to the line 2x-3y + 17 = 0.

A:

Q: Leª dx

A: We have to find the integral

Q: The function f(x) = = √x 2+√√4x is. increasing on its natural domain increasing on (2, 3) and…

A:

Q: fcos³ xdx from a = 0 to b = 3. 2

A:

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A:

Q: Find the tangent line approximation for √1+ x near x = 5. y = ||

A:

Q: Find the distance between the points. (Round your answer to two decimal places.) (9.1, −2.6),…

A:

Q: Given that f(-10) = -0.1 and f(-9.6) = 1.8, approximate f'(-10). f'(-10)

A: We know, f'(x)=f(x+∆x)-f(∆x)∆x Let, x=-10 and ∆x=0.4

Q: . Determine if AABC is a right-angled triangle, given A(1, 6, −2), B(2, 5, 3), and C(5, 3, 2).

A: Find the squares of all the sides of the triangle and then observe them

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A:

Q: Prove that √1+i√3+√1-i√3 = √6

A: