Let f(t) = √t. For a 0, find f'(a). f'(a) =

Q: Give a rule of the piecewise-defined function. Give the domain and the range. What is the rule?…

A:

Q: 4. [ sin* r cos* adr

A: Given integral:- ∫sin3xcos5xdx

Q: Question Evaluate the sum of the series Provide your answer below: n=0 n+1 53n-1 = n+1 53n-1 Enter…

A: Let's find sum of given series.

Q: The curve with parametric equations x = 2t cost, y = 2t sint, and z = 2t lies on z = x² + y². Select…

A:

Q: Use implicit differentiation to determine dy dx given the equation x² + y² = 3.

A:

Q: se that F(x) = f(g(x)) and g(3) = 6, g' (3) = 4, ƒ'(3) = 10, and ƒ'(6) = 7. Find F'(3).

A: Topic:- application of derivatives

Q: Find the derivative of the following function using the Fundamental Theorem of Calculus. F'(x) = €5x…

A: Let's find derivative of given integral function.

Q: A water tank in the shape of an inverted circular cone has a base radius of 2 m and height of 6 m.…

A: Let h meter be the height of the water at any time t. Let the angle of the cone be 2α Therefore, Tan…

Q: Find the absolute maximum and absolute minimum values of f on the given interval f(x) = x √4- x2…

A:

Q: LIM x to 09 tanh(x)/tan(x) using the L'hospital's rule

A:

Q: 1,5- 0 2 X √4-x² =dx 01-1 2

A:

Q: Show algebraically where the tangent line of the function r=1+cos theta is vertical and where the…

A:

Q: Sketch the region bounded by the graphs of the given equations and find the area of their region. X…

A:

Q: Exercise 2.6: Another infinite sum that generates 7 is given by 1 1 1 + - 5 Solving for 7, we obtain…

A:

Q: Find the critical numbers h(x) = (x-1) / (x2 + 4) *please use handwriting not typing, I understand…

A: Given query is to find critical points

Q: Factor f(x) into linear factors given that k is a zero of f(x). f(x)=x+3x³-30x²-124x-120; k=-2…

A:

Q: d dx f(x) = ex, f(0) = 8.

A:

Q: Where did you get y^2=((2a^2)/3)

A:

Q: Which of the following is a proper substitution to solve the Bernoulli's equation Select one: O None…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find dy/dx. y=x-4

A:

Q: WORK PROBLEMS (. You need to provide a clear and detailed solution for the following Questions: )…

A:

Q: If f(x, y, z) = xe² sin (42), then the gradient is Vf(x, y, z) =

A:

Q: Find the vertex, focus, and directrix of the parabola. x² = 6y vertex focus directrix (x, y) (x, y)…

A:

Q: View the curve (y - x)² + 2 = xy-3 as a contour of f(x, y). (a) Use f(-3, -2) to find a vector…

A:

Q: Find the slope of the tangent line to the curve - x² − 3xy + y³ = 1 at the point (2, 1). Question…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  and the given…

Q: In order to solve the following Bernoulli's equation dy dx we use the substitution e+3 Select one:…

A:

Q: For what value of c is the function f(x) = C= C 2-1 (x+1)(x-3) z=-1 z = 1 otherwise continuous at x…

A:

Q: Halley's law states that the barometric pressure (in inches of mercury) at an altitude of x mi above…

A:

Q: Prove that for all values of λ and u, the planes 4x 3y 5+μ a b 2x y 2z x 2y 2+2+²-1+2 ² 2 ²-2) = 0 -…

A:

Q: Solve the initial value problem for r as a vector function of t. d²r Differential equation: = -34k…

A:

Q: For the function, do the following. f(x) = 3/1/2 from a 1 to b = 3. Approximate the area under the…

A: We have to find the area using the two methods 1)Riemann sum using 10 rectangles 2) using definite…

Q: A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The material…

A: A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The material…

Q: 3) The price of a house is $500,000. You make a down payment of $50,000 and take a 30-year mortgage…

A: Let's find monthly payment, total amount paid and interest over the life of the loan.

Q: 0.5t Find the time 42 59 The concentration of a drug t hours after being injected is given by C'(t)…

A: Given query is to find the time when concentration is maximum.

Q: a) show that Sab = b) let c) find the solution set of 670 (ra) (56) where s.t. b 1 Show that Lio (x)…

A: Since you have posted multiple questions, we are supposed to answer only first  question. If you…

Q: A hexagon is a six sided regular polygon, or a 6-gon. Repeat the process above for inscribing a…

A: We have to find the area of hexagon.

Q: Use linear approximation to approximate√64.2 as follows. Let f(x)=√x. The equation of the tangent…

A: Topic- Linear Approximations We are given f(x)=xWe know thatL(x)=f(a)+f'(a)(x-a)ddxx=12x

Q: Find the integral using an appropriate trigonometric substitution. S 1 x² √√x² +25 dx O √x² +25 +C…

A:

Q: Solve the following DE: (1+ y² + xy²) dx + (x²y + y + 2xy) dy=0 O2y²+x²(1+x)²=C O 2y²+x²(y + x)² =c…

A:

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

A: Given query is to apply rolle's theorem.

Q: The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest…

A:

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 2 ft^3/min. How…

A:

Q: that has been recently. There is a been manufactured. The temperature is represented by T (t). the…

A:

Q: a) Find the linear approximating polynomial for the following function centered at the given point…

A:

Q: The dosage for a certain type of chemotherapy drug depends on several parameters of the particular…

A: We have to find the formulas for D and c that give D as a function of​ c, and c as a function of w.

Q: (7 y² +6 x)dx + 11 x y dy=0 (*) a) Determine whether the given differential equation (*) is exact…

A:

Q: Consider the function f(x) = ²/2 + x²/12 + x²/2 - 3x (a) Use the Intermediate Value Theorem to show…

A:

Q: c) = 5) =

A: Topic:- application of derivatives

Q: Find dy/dx. y=3x7

A:

Q: For the series -2 + 3 + (-9/2) + 27/4 + …, S14 =

A: It is a Geometric Progression where first term is -2 and common ratio is -1.5