The normal line to a curve h(x) = -x² + 1 at point Z, is defined as a line that passes through point Z and is perpendicular to the tangent line at point Z. Suppose that point Z is given as (2, -3), find an equation of the normal line to the curve at that given point.

Q: What is the derivative of y = sin (x³ sin (x³ – 3x)?

A:

Q: Solve the given differential equation by separation of variables. dy xy + 3x - y - 3 dx xy - 2x + 4y…

A:

Q: Evaluate the given limit. Show your complete solution. limo(-x ln(sin(4x² - x)))

A: Let's find limit of given function.

Q: dx S x²(x²+x+1) √ √ex - 1dx

A:

Q: f(x) == What is 1 a) Consider the function its domain? b) Now consider the function g(x, y) = ².…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

Q: What is S (x² + 2x)² dx? + x³ + ³x² + C 4 S (x² + 2x)²dx = ¹x¹ + x³ + 4 f (x² + 2x)²dx = (x² + 2x)¹…

A: We know, ∫xndx= xn+1/(n+1)

Q: Which of the following represents the symbol for the indefinite integral? S dx dy b a Σ

A:

Q: the base radius and height of a right circular cone are measured as 10 cm and 25 cm, respectively,…

A:

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: For a particular function, the derivative is given by f'(x) = (x+3)(x-1)². Determine the x-values…

A: Topic = Derivative

Q: find the derivative:  c(x)=(x2)500x (the choices are in the image bellow)

A: This question is based on Chain rule differentiation. d/dx {f(x).g(x)} = g(x).d/dx{f(x)} +…

Q: x-2x +x= 15; x (0) = 7, x (0) = -16 hand written plz

A:

Q: Given the graph below, what can you say about the function at x = -2? -10 Not Continuous Continuous

A:

Q: The graph above is a transformation of the function f(x) = Write an equation for the function…

A:

Q: 2x S x5 e ²x dx

A:

Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: Given x=t-4To find L{x.e-x}

Q: Which function is Chain Rule most useful for? Composite function Polynomial function Logarithmic…

A:

Q: What is the equation of the tangent line to the curve y=x^ +2x −x+8 where x = 1? y = 7x - 3 y = 7x…

A:

Q: 1. Let A = 24 12 -40 20 and consider the linear system = AY. Let Y(t) be the solution 5 What is the…

A: answer is in next step.  i can answer only one  question as per guideline thank you.

Q: sin 2x dx 4. J2osin cosmetin2xdx

A:

Q: C

A:

Q: What is the limit of limx→ sin x? 1/2 1 -1 10

A: Given

Q: Gym A Gym B Total Monthly Cost vs. Number of Visits C Number of Visits Total Monthly Cost 10 55 70-…

A: Linear cost

Q: x-2x +x= 15; x (0) = 7, x (0) = -16

A:

Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: Trapezoidal rule:-∫abf(x)dx=∆x2{f(x0)+2f(x1)+2f(x2)+...+2f(xn-1)+f(xn)}where ∆x=b-an, n is the…

Q: Q4/ Answer two from the following :- 4- Evaluate and change the order of integration in 1 = ²*xy…

A:

Q: What is the derivative of y = √/x? 1x² X 2 2 1 X X 2 23

A:

Q: The differential equation y""+ay""+by" + cy + dy = 0 6t has a solution y 2tet 6e sin(3t) for real…

A:

Q: A. Find the volume generated by rotating the region bounded by y=x, y=1 and the y-axis rotated about…

A:

Q: Using the concept of the derivative of sin x, what is the antiderivative of sin x? -2 cos x + C 2…

A: We know that: ddx(cos x)=-sin x...(1)

Q: Write the given system in the form x' = P(t)x+ f(t). x' = 4x+6y + 8 et y' = 8x-y-t¹ D-AD-41 C

A:

Q: 16. True or False: (a). Every element in a cyclic group (G) is a generator of G. (b). A group (G, *)…

A:

Q: Which of the following planes is the equation for the plane with an x-intercept at P(2,0,0), a…

A: The simple use for plane and point and normal vector..

Q: Given the piecewise function f(x) = = Why is f not differentiable at x = 0? f is discontinuous at x…

A:

Q: dx X २ Assume that x and I are differentiable functions of t, and 3xx -x ³² + y² = @ 3 Find dx (xc)…

A:

Q: d.w. Find the lengths for the - r = 1 + cosa

A: Given: r=1+cosθ

Q: Solve the following initial value problem using Laplace transform d'y dy dt -2y = 6e³t; dt² y (0) =…

A:

Q: -0.5 1 100³S 1-=X² dx represents the area of a region bounded by 1 O a. the vertical lines x = +0.5,…

A:

Q: If a person's temperature after x hours of strenuous exercise is T(x) = x³ (7- x²) + 98.6 degrees…

A: We have to calculate the rate of change after 1 hours

Q: -0.51-2-5)dy represents the area of a region bounded by O a. the curve x = 12, the line x = 5, and…

A: We have to choose the correct option

Q: 50° 60° 70° ?

A: To find the measure of the unknown angle in the following figure.

Q: What is the derivative 7 of y = (3x + 1)²? 21 dx dy = 6 (3x + 1)²¹ dx = dy 6 (3x + 1)² dx = 7 (3x +…

A:

Q: Give the general equation of the plane containing the point (3,-1,4) and 2-2 -3 4. | perpendicular…

A: given plane pass through the point(3,-1,4)

Q: What is f 5√xdx? 3 f 5√√xdx = 5x² + C 2 3 f5√xdx = 10x² + C 3 f5√xdx = 5x² + C 3 [ 5vxdx= 5x? +C

A: Let's solve given integral.

Q: Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1.

A: The function f(x) is given by, f(x)=ln(3-2x) Differentiating the function successively upto n…

Q: Use the chain rule to find the indicated partial derivatives. z = x4 + x²y, x = s + 2t - u, y = stu2…

A:

Q: Q.2)(A) Find a formula for the area of the triangle in the xy-plane with vertices at A(0, 0), B(a₁,…

A:

Q: Using the graph of the exponential function below, what is the limx→12 (3x)? 8 0 2 6

A:

Q: Use the graph below to answer the question below: 5 4 y = f(x) 1 2 Find lim f(z). Be sure to read…

A:

Q: Find y' y = e2x - e3x e4x

A: This question is based on diffrentiation of exponential Function.