Prove the following equations are identities for all permissible values of x, by manipulating only the left side of each equation. sin x + tan x sin x 1+ secx 1 1 1+sinx 1-sinx = 2 sec² x

Q: 3a) Determine whether or not the function below is differentiable at O by using the definition of…

A:

Q: Find the slope of the curve y = cos The slope of the curve is (Type an exact answer.) ¹x at √3 T 2'6…

A:

Q: 2. Differentiate a) each of the following functions. Leave in unsimplified form. b) f(x) =…

A: 2)a) y=x6+5 sqrt(x)b) f(x)=3sinx - cos4xDifferenciate the given functions.

Q: q 22. 16 determine the magnitude and direction of the vector v = and also show that  v = |v|u ,…

A:

Q: Find the linearizations L(x,y,z) of the function f(x,y,z) = 6xy + yz + 7xz at (1,1,1), (1,0,0), and…

A:

Q: Let f(x, y) = 3x² - 2x + 8y + 5y² - xy List the critical point: The critical point is a Select an…

A: We can find the critical point of the function .

Q: Write the following expression Ohm--h(m+3) O In (m) - In (m + 3) 2 In (m) - In (m+3) hm+=h(m+3) m as…

A: To write the following expression as a  sum and/or difference of logarithms without exponents.

Q: Find the inflection point given the function F(x) = f e-t² dt. No graphs.

A: Given function: To find : Inflection point of F(x)

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of…

A: Using differentiation

Q: Express the function G in the form fo g. (There is more than one correct answer. The function is of…

A:

Q: (d²x) Q²: L {1²} dt² =?

A:

Q: A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a…

A:

Q: Determine the value(s) of x for which f(x) = -3x² - 5x20 has a horizontal tangent line. If there is…

A:

Q: for what value of the number k does the function f(x)= (1+kx+x^2)e^x have f'(0) =3

A:

Q: What is the limit lim x→3 √x³ - 2-5 x - 3 3 27 10 9 10 +∞ Does not exist ?

A: Given

Q: (iii) Consider the function C(Q₁, Q₂)=Q-30102+Q2. What level of Q₁ and Q₂ locally minimise this…

A: According to our guidelines , we can answer only first question (due to multiple questions). Kindly…

Q: The terminal ray of angle drawn in standard position passes through (2, -3). What is the value of…

A: given the terminal ray of angle  drawn in standard position passes through (2,-3)

Q: Consider the curve given by x³ + y³ = xy² + 1. Find the slope of the tangent line to the curve at…

A: given

Q: 4. Show that 2y"-y'-y=0 when y=e* + e.

A:

Q: (x = 2+t 10. Given L₁: y = 1-t;t ER and L₂: F (3,0,-1) + s(2,3,-1); SER z = t a) Determine whether…

A:

Q: The population of a slowly growing bacterial colony after t hours is given by p(t) = 3t² + 21t +…

A:

Q: 3. Differentiate and simplify in fully factored form. a) f(x) = (1+x²2) 3 b) y = (3x² + 4)²(3 + x³)5

A:

Q: a. Find the arc length function for F(t). s(t) = b. Find the arc length parameterization for r(t).…

A:

Q: 27. cos5 x sin³ x 3 si dx

A:

Q: A region bounded by f(x) = 5 - x, y = 1, and x = 1 is shown. What is the volume of the solid formed…

A:

Q: A local business has a Cost function given by of students enrolled. Find the average rate of change…

A: The average rate of change of a function f(x) from x=a to x=b is

Q: Write the following in exponential form: y = In(0.34) O 3.4⁰ = y O e = 0.34 O e³.4 = y O 3.4 = e

A: The given equation is; y=ln(0.34)Write in exponential form.

Q: dy = x³ where y = 7 when x = 0. dx What is the value of y when x = 4 to significant figures? 12 15…

A:

Q: Determine vector and parametric equations for the line with z-intercept 4 and is parallel to the…

A:

Q: A cheesecake has equally sized slices. Each slice is a different flavor. The diameter of the…

A:

Q: Let f(x) = In(x) and g(x) = log3x. For all x>1, f(x) < g(x) O True O False

A:

Q: Given f(x, y) = 10√/8x5 + 7y + 2xy, find fz(x, y) = fy(x, y) =

A:

Q: Find an equation for the plane that is tangent to the surface z = In (x³ +y³) at the point P(0,1,0).

A:

Q: practice question - 11.32 Gwanda has the following equation for a sphere: (x^2) + (y^2) +(z^2) -…

A:

Q: It is determinate because there is only one known force. It is determinate because there are no…

A:

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(4,0,4) on the…

A:

Q: Consider the curve y = x² + 3x + 5. Find the slope of the secant line at the point where x = 9. Oh…

A:

Q: 5. Find the absolute maximum of f(x) = x¹e-77 on [0,4]

A: The given function is,

Q: Let f(x) = In(x) and g(x) = log2x. For all 0 g(x) O True O False

A:

Q: Suppose that f(x, y) = x² + y²¹ — 2xy Then the minimum is

A: We need to find minimum of function.

Q: 8. Determine the equation of the tangent line to the curve y = -x² − 3x + 4 at x = 2.

A:

Q: Find the first partial derivatives of the following function. s+ 3t s-t f(s,t)=-

A:

Q: Consider the plane with a scalar equation 4x-2y+z-19=0. Find the point of intersection of this plane…

A:

Q: Use the partial-fraction method to solve the following equation. dy dx = (y + 5)(y-10), where y(0) =…

A:

Q: Find f(a), f(a+h), and the difference quotient _f(a + h) − f(a), where h‡ 0. h f(x) = 9x² + 8 f(a)…

A:

Q: Find the volume of the tetrahedron shown using the order dz dx dy. The tetrahedron is bounded by the…

A: The tetrahedron is bounded by the planes Now, from above data limit of z is:-Now, we need to find…

Q: f=i-j g= 12i+ 3j Find: -4f-10g

A:

Q: Determine whether the following improper integral converges and, if it does, calculate it: S [Hint:…

A:

Q: 21. a) Evaluate the following limits. Show proper steps. 8x²-2x-3 2x+1 a) lim x→→ 2 2x x-0 √2x+1-1…

A:

Q: 1. Determine vector and parametric equations for the line with z-intercept 4 and is parallel to the…

A: To determine the vector and parametric equations for the line with -intercept 4 and is parallel to…