DI-related instability when using HttpClientFactory

#### Investigative information

- Timestamp: February 3rd, 2020, ~5:40PM CST
- Function App version: ~3, Runtime version: 3.0.13107
- Function App name: (will provide if needed)
- Function name(s) (as appropriate): (will provide if needed)
- Invocation ID: (will provide if needed)
- Region: Central US

#### Repro steps

I'm referencing the following nuget packages:
```xml




all
runtime; build; native; contentfiles; analyzers; buildtransitive



all
runtime; build; native; contentfiles; analyzers; buildtransitive




```

I'm using Microsoft.Azure.Functions.Extensions for DI like so:
```csharp
public class Startup : FunctionsStartup
{
public override void Configure(IFunctionsHostBuilder builder)
{
builder.Services.AddHttpClient();
builder.Services.AddScoped();
}
}
```

And the service looks something like this:
```csharp
public class ApiService : IApiService
{
private readonly IHttpClientFactory _httpClientFactory;

public ApiService(IHttpClientFactory httpClientFactory)
{
_httpClientFactory = httpClientFactory;
}

public void MakeRequest()
{
var httpClient = _httpClientFactory.CreateClient();
httpClient.PostAsync(...);
}
}
```

And the function looks something like this:
```csharp
public class MyTrigger
{
private readonly IApiService _apiService;

public MyTrigger(IApiService apiService)
{
_apiService = apiService;
}

[FunctionName("MyTrigger")]
public void Run([TimerTrigger("0 */5 * * * *", RunOnStartup = true)]TimerInfo timerInfo, CancellationToken cancellationToken)
{
foreach (var x in alot)
{
_apiService.MakeRequest();
}
}
}
```

Here's the error message and stack trace I see in App Insights:
```
Scope disposed{no name, Parent=disposed{no name, Parent={no name, Parent={no name}}}} is disposed and scoped instances are disposed and no longer available.

DryIoc.ContainerException:
at DryIoc.Throw.It (Microsoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=nullMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: D:\a\1\s\src\WebJobs.Script.WebHost\DependencyInjection\DryIoc\Container.csMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: 8990)
at DryIoc.Scope.TryGet (Microsoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=nullMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: D:\a\1\s\src\WebJobs.Script.WebHost\DependencyInjection\DryIoc\Container.csMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: 7880)
at DryIoc.Container+InstanceFactory.GetAndUnwrapOrDefault (Microsoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=nullMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: D:\a\1\s\src\WebJobs.Script.WebHost\DependencyInjection\DryIoc\Container.csMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: 1479)
at DryIoc.Container+InstanceFactory.GetInstanceFromScopeChainOrSingletons (Microsoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=nullMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: D:\a\1\s\src\WebJobs.Script.WebHost\DependencyInjection\DryIoc\Container.csMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: 1465)
at DryIoc.Container.DryIoc.IResolver.Resolve (Microsoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=nullMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: D:\a\1\s\src\WebJobs.Script.WebHost\DependencyInjection\DryIoc\Container.csMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: 307)
at lambda_method (Anonymously Hosted DynamicMethods Assembly, Version=0.0.0.0, Culture=neutral, PublicKeyToken=null)
at DryIoc.Container.ResolveAndCacheDefaultFactoryDelegate (Microsoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=nullMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: D:\a\1\s\src\WebJobs.Script.WebHost\DependencyInjection\DryIoc\Container.csMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: 223)
at DryIoc.Container.DryIoc.IResolver.Resolve (Microsoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=nullMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: D:\a\1\s\src\WebJobs.Script.WebHost\DependencyInjection\DryIoc\Container.csMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: 194)
at Microsoft.Azure.WebJobs.Script.WebHost.DependencyInjection.ScopedServiceProvider.GetService (Microsoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=nullMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: D:\a\1\s\src\WebJobs.Script.WebHost\DependencyInjection\ScopedServiceProvider.csMicrosoft.Azure.WebJobs.Script.WebHost, Version=3.0.0.0, Culture=neutral, PublicKeyToken=null: 25)
at Microsoft.Extensions.DependencyInjection.ServiceProviderServiceExtensions.GetRequiredService (Microsoft.Extensions.DependencyInjection.Abstractions, Version=3.1.0.0, Culture=neutral, PublicKeyToken=adb9793829ddae60)
at Microsoft.Extensions.DependencyInjection.ServiceProviderServiceExtensions.GetRequiredService (Microsoft.Extensions.DependencyInjection.Abstractions, Version=3.1.0.0, Culture=neutral, PublicKeyToken=adb9793829ddae60)
at Microsoft.Extensions.Http.DefaultHttpClientFactory.CreateHandlerEntry (Microsoft.Extensions.Http, Version=3.1.0.0, Culture=neutral, PublicKeyToken=adb9793829ddae60)
at Microsoft.Extensions.Http.DefaultHttpClientFactory+<>c__DisplayClass14_0.<.ctor>b__1 (Microsoft.Extensions.Http, Version=3.1.0.0, Culture=neutral, PublicKeyToken=adb9793829ddae60)
at System.Lazy`1.ViaFactory (System.Private.CoreLib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=7cec85d7bea7798e)
at System.Lazy`1.ExecutionAndPublication (System.Private.CoreLib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=7cec85d7bea7798e)
at System.Lazy`1.CreateValue (System.Private.CoreLib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=7cec85d7bea7798e)
at System.Lazy`1.get_Value (System.Private.CoreLib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=7cec85d7bea7798e)
at Microsoft.Extensions.Http.DefaultHttpClientFactory.CreateHandler (Microsoft.Extensions.Http, Version=3.1.0.0, Culture=neutral, PublicKeyToken=adb9793829ddae60)
at Microsoft.Extensions.Http.DefaultHttpClientFactory.CreateClient (Microsoft.Extensions.Http, Version=3.1.0.0, Culture=neutral, PublicKeyToken=adb9793829ddae60)
at System.Net.Http.HttpClientFactoryExtensions.CreateClient (Microsoft.Extensions.Http, Version=3.1.0.0, Culture=neutral, PublicKeyToken=adb9793829ddae60)
```

#### Expected behavior

I expect HttpClientFactory to be supported and stable for Azure Functions v3.

#### Actual behavior

It went well for a good 1k+ requests, but eventually it bombed out with essentially the same error as seen in #5060. Unlike that issue however, I'm injecting HttpClientFactory instead of HttpClient like was recommended in the comments and calling factory.CreateClient() each time a request needs to be made. Looks like #5074 may have been a reproduction of this as well. Is there something else I should be doing in the code to avoid this bizarre issue?

#### Known workarounds

I switched back to the old school approach of a static HttpClient and that works well enough for my needs, but I'm assuming HttpClientFactory is the way of the future.

Start with the Azure Functions v3 reproduction and the stack trace through ScopedServiceProvider.cs, DryIoc Container.cs, and DefaultHttpClientFactory.CreateHandler. Investigate why CreateClient() reaches a disposed scope after repeated requests; done means identifying the lifecycle failure and adding a regression test showing stable HttpClientFactory use.

Written by the indexing model from the issue text.